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Arithmetic Geometric And Harmonic Progression Pdf Free
Arithmetic Geometric And Harmonic Progression Pdf Free

 

Arithmetic Geometric And Harmonic Progression Pdf Free http://shurll.com/bigil

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Use,,,in,,,geometry[edit].,,,The,,constant,,difference,,is,,commonly,,known,,as,,common,,difference,,and,,is,,denoted,,by,,d.,,Your,score,will,be,emailed,to,you.Questions:,MCQ,Quiz,for,Geometric,ProgressionsGoogle,DocumentAnswer,Submission,Form,for,MCQ,Quiz,#3Answer,Submission,Form:,Geometric,Progression,MCQGoogle,Spreadsheet,Form,MCQ,Quiz/Worksheet,#4Harmonic,Progressions.Fill,up,the,answers,in,the,Answer,Submission,Form,below,this,Question-Paper,document.,12,,6,,4,,3,,12,5,{displaystyle,{tfrac,{12}{5}}},,,2,,,,,12,1, ,n,{displaystyle,{tfrac,{12}{1 n}}},.,Your,,score,,will,,be,,emailed,,to,,you.Questions:,,Harmonic,,ProgressionGoogle,,DocumentAnswer,,Submission,,Form,,for,,MCQ,,Quiz,,#4Answer,,Submission,,Form:,,Harmonic,,ProgressionGoogle,,Spreadsheet,,Form,,MCQ,,Quiz/Worksheet,,#5More,,on,,Harmonic,,ProgressionMCQ,,Quiz:,,Harmonic,,ProgressionGoogle,,Spreadsheet,,Form,,MCQ,,Quiz/Worksheet,,#6Mixed,,ProgressionsMCQ,,Quiz:,,Harmonic,,ProgressionGoogle,,Spreadsheet,,Form,,You,,might,,like,,to,,take,,a,,look,,at,,our,,other,,algebra,,tutorials:Introduction,,to,,Complex,,NumbersIntroduction,,to,,Complex,,Numbers,,and,,iota.,,This,,mathematics-related,,article,,is,,a,,stub.,,44,,,.,,,$a{m,,, ,,,1},,,=,,,am,,, ,,,d$,,,,,,nth,,,term,,,of,,,AP,,,The,,,nth,,,term,,,of,,,arithmetic,,,progression,,,is,,,given,,,by,,,$an,,,=,,,a1,,, ,,,(n,,,-,,,1)d$,,,,,,or,,,in,,,more,,,general,,,term,,,,it,,,can,,,be,,,written,,,as,,,$an,,,=,,,am,,, ,,,(n,,,-,,,m)d$,,,,,,Sum,,,of,,,n,,,terms,,,of,,,AP,,,The,,,sum,,,of,,,the,,,first,,,n,,,terms,,,of,,,arithmetic,,,progression,,,is,,,n,,,times,,,the,,,average,,,of,,,the,,,first,,,term,,,and,,,the,,,last,,,term.,,,(Terms,,in,,the,,form,,x,,y,, ,,z,,,,{displaystyle,,{frac,,{x}{y z}},,},,can,,be,,expressed,,as,,x,,y,,y,, ,,z,,y,,{displaystyle,,{frac,,{frac,,{x}{y}}{frac,,{y z}{y}}}},,,,,we,,can,,let,,x,,y,,=,,a,,{displaystyle,,{frac,,{x}{y}}=a},,and,,z,,y,,=,,k,,d,,{displaystyle,,{frac,,{z}{y}}=kd},,.).,,1,,,a,,,,,,,,,,1,,,a,,, ,,,d,,,,,,,,,,1,,,a,,, ,,,2,,,d,,,,,,,,,,1,,,a,,, ,,,3,,,d,,,,,,,,,,⋯,,,,,,,1,,,a,,, ,,,k,,,d,,,,,,,{displaystyle,,,{frac,,,{1}{a}},,,,{frac,,,{1}{a d}},,,,{frac,,,{1}{a 2d}},,,,{frac,,,{1}{a 3d}},,,,cdots,,,,{frac,,,{1}{a kd}},},,,.,,,the,,,learning,,,point,,,Search,,,this,,,site,,,HomeMathArithmetic,,,,Geometric,,,,Harmonic,,,Progressions,,,(Tutorial,,,on,,,AP,,,,GP,,,,HP,,,,AM,,,,GM,,,,HM,,,and,,,Series,,,Summations)-,,,With,,,Solved,,,Problems,,,,MCQ,,,QuizzesTrigonometry,,,1a,,,-,,,Angles,,,in,,,Degrees,,,and,,,Radians,,,,Introduction,,,to,,,Trigonometric,,,Ratios,,,,Domains,,,and,,,ranges,,,,Basic,,,Identities,,,,Compound,,,Angle,,,Formulas,,,,Double,,,and,,,Triple,,,Angle,,,FormulasTrigonometry,,,1b,,,-,,,Solved,,,problems,,,related,,,to,,,Basic,,,Trigonometric,,,Ratios,,,,Degrees,,,and,,,Radians,,,,Domains,,,and,,,ranges,,,,Basic,,,Identities,,,,Compound,,,Angle,,,Formulas,,,,Double,,,and,,,Triple,,,Angle,,,FormulasTrigonometry,,,2a,,,-,,,Basic,,,concepts,,,related,,,to,,,Heights,,,and,,,Distances,,,,Angles,,,of,,,Elevation,,,and,,,Depression,,,,Sine,,,and,,,Cosine,,,Rules,,,,Circumcircle,,,,Incircle,,,and,,,Escribed,,,circleTrigonometry,,,2b,,,-,,,Heights,,,and,,,Distances,,,,Angles/Sides,,,of,,,Triangles,,,,Angles,,,of,,,Elevation,,,and,,,Depression,,,,Sine,,,and,,,Cosine,,,Rules,,,,Circumcircles,,,,Incircle,Escribed,,,circles,,,-,,,Problems,,,,Solutions,,,,MCQ,,,QuizzesTrigonometry,,,3a,,,Inverse,,,Trigonometric,,,Ratios,,,-,,,arc-sin,,,,arc-cos,,,,arc-tan;,,,Domains,,,and,,,Ranges,,,,Principal,,,Value,,,Branches,,,,Important,,,Relations,,,and,,,FormulasTrigonometry,,,3b,,,(,,,Solved,,,Problems,,,and,,,companion,,,MCQ,,,Tests,,,related,,,to,,,Inverse,,,Trigonometric,,,Ratios,,,)Quadratic,,,Equations,,,,Cubic,,,and,,,Higher,,,Order,,,Equations,,,-,,,Using,,,Factorization,,,and,,,Formula-,,,A,,,tutorial,,,with,,,solved,,,problems,,,and,,,a,,,QuizPrinciple,,,of,,,Mathematical,,,Induction-,,,A,,,Tutorial,,,with,,,solved,,,problems-,,,Identities,,,involving,,,Natural,,,Numbers,,,,Trigonometric,,,RatiosComplex,,,Numbers-,,,Introductory,,,Tutorial,,,,Examples,,,,Solved,,,Problems,,,,MCQ,,,Quiz,,,-,,,Argand,,,Plane,,,,Roots,,,of,,,Unity,,,,Basic,,,OperationsCalculus,,,-,,,Differential,,,Calculus,,,-,,,Solved,,,Problem,,,Set,,,I,,,and,,,MCQ,,,Quiz,,,-,,,Algebraic,,,,exponential,,,,logarithmic,,,,trigonometric,,,,polynomial,,,functionsCalculus,,,-,,,Introducing,,,Integral,,,Calculus,,,-,,,Definitions,,,and,,,Formulas,,,-,,,Indefinite,,,and,,,Definite,,,Integrals,,,,Substitution,,,,Integration,,,by,,,Parts,,,,Reduction,,,Formulas,,,and,,,Summation,,,of,,,SeriesPermutations,,,and,,,CombinationsLinear,,,Algebra,,,-,,,Problems,,,Based,,,on,,,Simultaneous,,,Equations,,,,Eigenvalues,,,,EigenvectorsProbability:,,,Part,,,1,,,-,,,Some,,,Definitions,,,with,,,A,,,Solved,,,Problem,,,Set-,,,Continuous,,,and,,,Discrete,,,Random,,,Variables,,,,Chebyshev,,,InequalityProbability,,,Distributions-,,,Discrete,,,and,,,Continuous-,,,with,,,examples-,,,Bernouilli/Binomial/Geometric/Uniform/Exponential/Gamma,,,,etc.PhysicsBasic,,,Mechanics:,,,Introduction,,,to,,,Vectors,,,and,,,MotionBasic,,,Mechanics:,,,More,,,on,,,Vectors,,,and,,,Projectile,,,MotionBasic,,,Mechanics:,,,Newton's,,,Laws,,,of,,,MotionBasic,,,Mechanics:,,,Work,,,,Force,,,and,,,EnergyBasic,,,Mechanics:,,,Simple,,,Harmonic,,,MotionBasic,,,Mechanics:,,,Rotational,,,DynamicsBasic,,,Mechanics:,,,Fluid,,,MechanicsEngineering,,,MechanicsEngineering,,,Mechanics:,,,Moments,,,and,,,Equivalent,,,SystemsEngineering,,,Mechanics:,,,Centroids,,,and,,,Center,,,of,,,GravityEngineering,,,Mechanics:,,,Analysis,,,of,,,StructuresBasic,,,Electrostatics,,,and,,,ElectromagnetismBasic,,,Electrostatics:,,,An,,,IntroductionBasic,,,Electrostatics:,,,Some,,,Interesting,,,ProblemsBasic,,,Electromagnetism:,,,An,,,IntroductionMechanicsBasic,,,Electromagnetism:,,,Some,,,Interesting,,,ProblemsElectrostatics,,,and,,,Electromagnetism:,,,A,,,Quick,,,Look,,,at,,,More,,,Advanced,,,ConceptsChemistryAtomic,,,Structure:,,,Notes,,,,Tutorial,,,,Problems,,,with,,,SolutionsStoichiometryChemical,,,KineticsChemical,,,EquilibriumAn,,,Introduction,,,to,,,ElectrochemistryLiquid,,,SolutionsThe,,,Gaseous,,,StateCo-ordination,,,CompoundsNomenclature,,,of,,,Simple,,,Organic,,,CompoundsAlkanes,,,,Alkenes,,,,AlkynesBasic,,,Organic,,,ReactionsComputer,,,ScienceThe,,,Book,,,Corner,,,for,,,Computer,,,Science,,,and,,,Programming,,,EnthusiastsProgramming,,,InterviewsArrays,,,and,,,Searching:,,,Binary,,,Search,,,(,,,with,,,C,,,Program,,,source,,,code)Arrays,,,and,,,Sorting:,,,Insertion,,,Sort,,,(,,,with,,,C,,,Program,,,source,,,code,,,,a,,,tutorial,,,and,,,an,,,MCQ,,,Quiz,,,on,,,Sorting)Arrays,,,and,,,Sorting:,,,Selection,,,Sort,,,(C,,,Program/Java,,,Program,,,source,,,code,,,,a,,,tutorial,,,and,,,an,,,MCQ,,,Quiz,,,on,,,Sorting)Arrays,,,and,,,Sorting:,,,Merge,,,Sort,,,(,,,C,,,Program/Java,,,Program,,,source,,,code,,,,a,,,tutorial,,,and,,,an,,,MCQ,,,Quiz,,,on,,,Sorting)Arrays,,,and,,,Sorting:,,,Quick,,,Sort,,,(C,,,Program/Java,,,Program,,,source,,,code;,,,a,,,tutorial,,,and,,,an,,,MCQ,,,Quiz,,,)Data,,,Structures:,,,Stacks,,,(,,,with,,,C,,,Program,,,source,,,code)Data,,,Structures:,,,Queues,,,(,,,with,,,C,,,Program,,,source,,,code)MCQ,,,Quizzes,,,on,,,Data,,,Structures,,,,Algorithms,,,and,,,the,,,Complexity,,,of,,,Algorithms-,,,Test,,,how,,,much,,,you,,,know!MCQ,,,Quizzes-,,,Test,,,how,,,much,,,you,,,know,,,about,,,basic,,,Algorithms,,,and,,,Data,,,Structures!MCQ,,,Quizzes-,,,Test,,,your,,,C,,,Programming,,,skills!:,,,Quiz,,,questions,,,on,,,Strings,,,,Arrays,,,,PointersLearning,,,Python:,,,Programming,,,and,,,Data,,,StructuresIntroduction,,,to,,,Ruby,,,and,,,some,,,playing,,,around,,,with,,,the,,,Interactive,,,Ruby,,,Shell,,,(irb)C,,,Program,,,(,,,Source,,,Code,,,and,,,Explanation),,,for,,,a,,,Single,,,Linked,,,ListC,,,Program,,,(Source,,,Code),,,for,,,a,,,Doubly,,,Linked,,,ListC,,,Program,,,(Source,,,Code,,,With,,,Documentation),,,-,,,Circular,,,Linked,,,ListIntroduction,,,to,,,Java,,,CollectionsNetworking:,,,Client-Server,,,and,,,Socket,,,Programming,,,(in,,,Python)Networking:,,,Client-Server,,,and,,,Socket,,,Programming,,,(in,,,Java)Intro,,,to,,,Digital,,,Image,,,Processing,,,(Basic,,,filters,,,and,,,Matlab,,,examples.)EEBasics,,,of,,,DC,,,CircuitsDC,,,Circuits:,,,An,,,IntroductionDC,,,Circuits:,,,Examples,,,and,,,Problems,,,,Circuits,,,with,,,Resistance,,,and,,,CapacitanceDC,,,Circuits:,,,Introducing,,,InductorsDC,,,Circuits:,,,Problems,,,related,,,to,,,RL,,,,LC,,,,RLC,,,CircuitsDC,,,Circuits:,,,Electrical,,,Networks,,,and,,,Network,,,TheoremsDC,,,Circuits:,,,More,,,Network,,,Theorems,,,,Examples,,,,Solved,,,ProblemsBasic,,,Digital,,,Circuits:,,,Number,,,System-1Basic,,,Digital,,,Circuits:,,,Number,,,System-2Basic,,,Digital,,,Circuits:,,,Boolean,,,Algebra-1Basic,,,Digital,,,Circuits:,,,Boolean,,,Algebra-2Basic,,,Digital,,,Circuits:,,,Karnaugh,,,Maps-1Basic,,,Digital,,,Circuits:,,,Karnaugh,,,Maps-2Basic,,,Digital,,,Circuits:,,,Combinational,,,Circuits-1Basic,,,Digital,,,Circuits:,,,Combinational,,,Circuits-2Basic,,,Digital,,,Circuits:,,,Sequential,,,Circuits-1Basic,,,Digital,,,Circuits:,,,Sequential,,,Circuits-2EnglishCBSE/ICSE/IITTop,,,Schools,,,&,,,School-wise,,,results,,,(CBSE,,,2015,,,Class,,,12,,,Examinations)Toppers,,,in,,,CBSE,,,Class,,,12,,,Exams,,,,2015Top,,,Schools,,,&,,,School-wise,,,Results,,,(ISC,,,2015,,,,Class,,,12,,,Exams)Toppers,,,in,,,ISC,,,Class,,,12,,,Exams,,,,2015Top,,,Schools,,,&,,,School-wise,,,Results,,,(RBSE,,,2015,,,Class,,,12,,,,Rajasthan,,,State)Top,,,Schools,,,&,,,School-wise,,,results,,,(CBSE,,,2014,,,Class,,,12,,,Examinations)Top,,,Schools,,,&,,,School-wise,,,Results,,,(ICSE-ISC,,,2014,,,Examinations)Top,,,Schools,,,&,,,School-wise,,,results,,,(ICSE-ISC,,,2013,,,Class,,,10,,,&,,,12,,,Examinations)IIT,,,JEE,,,Preparation,,,MaterialBuy,,,CBSE/NCERT,,,BooksISC,,,Class,,,12:,,,Syllabus,,,,Specimen,,,Papers,,,,BooksBooks,,,From,,,FlipkartA,,,List,,,of,,,CBSE,,,Schools,,,in,,,IndiaA,,,List,,,of,,,CBSE,,,Schools,,,in,,,DelhiA,,,List,,,of,,,CBSE,,,Schools,,,in,,,Uttar,,,PradeshA,,,List,,,of,,,CBSE,,,Schools,,,in,,,Andhra,,,PradeshA,,,List,,,of,,,CBSE,,,Schools,,,in,,,Tamil,,,NaduA,,,List,,,of,,,CBSE,,,Schools,,,in,,,HarayanaA,,,List,,,of,,,CBSE,,,Schools,,,in,,,PunjabA,,,List,,,of,,,CBSE,,,Schools,,,in,,,KarnatakaA,,,List,,,of,,,CBSE,,,Schools,,,in,,,KeralaA,,,List,,,of,,,CBSE,,,Schools,,,in,,,West,,,BengalA,,,List,,,of,,,CBSE,,,Schools,,,in,,,Madhya,,,PradeshA,,,List,,,of,,,CBSE,,,Schools,,,in,,,MaharashtraList,,,of,,,all,,,ICSE,,,and,,,ISC,,,Schools,,,in,,,India,,,(,,,and,,,abroad,,,).UP,,,Board,,,Madhyamik,,,SchoolsKerala-Board,,,HSE,,,SchoolsSchool,,,ListingsChhattisgarh,,,Board,,,CGBSEAboutPhotoBlog,,,-,,,Travel,,,PicsRandom,,,ThoughtsTop,,,ICSE,,,Schools,,,(City,,,Wise)Top,,,ICSE-ISC,,,Schools,,,in,,,AgraTop,,,ICSE-ISC,,,Schools,,,in,,,AhmedabadTop,,,ICSE-ISC,,,Schools,,,in,,,AllahabadTop,,,ICSE-ISC,,,Schools,,,in,,,Bangalore,,,(Bengaluru)Top,,,ICSE-ISC,,,Schools,,,in,,,DarjeelingTop,,,ICSE-ISC,,,Schools,,,in,,,Delhi,,,,Gurgaon,,,,NoidaTop,,,ICSE-ISC,,,Schools,,,in,,,DehradunTop,,,ICSE-ISC,,,Schools,,,in,,,ChennaiTop,,,ICSE-ISC,,,Schools,,,in,,,ChandigarhTop,,,ICSE-ISC,,,Schools,,,in,,,Mumbai,,,,Navi,,,Mumbai,,,and,,,ThaneTop,,,ICSE-ISC,,,Schools,,,in,,,HyderabadTop,,,ICSE-ISC,,,Schools,,,in,,,KanpurTop,,,ICSE-ISC,,,Schools,,,in,,,Kolkata,,,and,,,HowrahTop,,,ICSE-ISC,,,Schools,,,in,,,LucknowTop,,,CBSE,,,Schools,,,(City-Wise)Top,,,CBSE,,,Schools,,,in,,,VishakhapatnamTop,,,CBSE,,,Schools,,,in,,,ChennaiTop,,,CBSE,,,Schools,,,in,,,PuneTop,,,CBSE,,,Schools,,,in,,,Bangalore,,,(Bengaluru)Top,,,CBSE,,,Schools,,,in,,,Hyderabad,,,and,,,SecunderabadTop,,,CBSE,,,Schools,,,in,,,IndoreTop,,,CBSE,,,Schools,,,in,,,BhopalTop,,,CBSE,,,Schools,,,in,,,GuwahatiTop,,,CBSE,,,Schools,,,in,,,KolkataTop,,,CBSE,,,Schools,,,in,,,PatnaTop,,,CBSE,,,Schools,,,in,,,LucknowTop,,,CBSE,,,Schools,,,in,,,KanpurTop,,,CBSE,,,Schools,,,in,,,AjmerTop,,,CBSE,,,Schools,,,in,,,JaipurTop,,,CBSE,,,Schools,,,in,,,Ahmedabad,,,and,,,GandhinagarTop,,,CBSE,,,Schools,,,in,,,ChennaiTop,,,CBSE,,,Schools,,,in,,,ChandigarhTop,,,CBSE,,,Schools,,,in,,,DelhiAdvertise,,,With,,,Us,,,The,,,Learning,,,Point,,,>,,,Mathematics,,,>,,,,,,Arithmetic,,,,Geometric,,,,Harmonic,,,Progressions,,,(Tutorial,,,on,,,AP,,,,GP,,,,HP,,,,AM,,,,GM,,,,HM,,,and,,,Series,,,Summations)-,,,With,,,Solved,,,Problems,,,,MCQ,,,Quizzes,,,Target,,,Audience:,,,High,,,School,,,Students,,,,College,,,Freshmen,,,and,,,Sophomores,,,,Class,,,11/12,,,Students,,,in,,,India,,,preparing,,,for,,,ISC/CBSE,,,and,,,Entrance,,,Examinations,,,like,,,the,,,IIT-JEEMain,,,or,,,Advanced/AIEEE,,,,and,,,anyone,,,else,,,who,,,needs,,,this,,,Tutorial,,,as,,,a,,,reference!After,,,reading,,,this,,,tutorial,,,you,,,might,,,want,,,to,,,check,,,out,,,some,,,of,,,our,,,other,,,Mathematics,,,Quizzes,,,as,,,well.,,,where,,a/d,,is,,not,,a,,natural,,number,,and,,k,,is,,a,,natural,,number.,,,,Relationship,,between,,arithmetic,,,geometric,,,and,,harmonic,,means,,$AM,,times,,HM,,=,,GM^2$,,,,Suggested,,Readings,,You,,may,,be,,interested,,in,,the,,following,,Derivation,,of,,formulas,,of,,arithmetic,,progression,,Derivation,,of,,formulas,,for,,finite,,and,,infinite,,geometric,,progression,,Derivation,,of,,the,,relationship,,between,,arithmetic,,,geometric,,,and,,harmonic,,means,,,,Tags:arithmetic,,progressiongeometric,,progressioninfinite,,geometric,,progressionharmonic,,progression,,Geometric,,progression,,with,,some,,given,,termsThree-digit,,numbers,,not,,divisible,,by,,3,,,,Problem,,10,,,,Special,,Products,,and,,Factoring,,up,,Geometric,,progression,,with,,some,,given,,terms,,,,Log,,in,,or,,register,,to,,post,,comments,,110183,,reads,,SPONSORED,,LINKS,,Algebra,,Laws,,of,,Exponents,,and,,RadicalsLogarithm,,and,,Other,,Important,,Properties,,in,,AlgebraQuadratic,,Equations,,in,,One,,VariableSpecial,,Products,,and,,FactoringArithmetic,,,geometric,,,and,,harmonic,,progressionsGeometric,,progression,,with,,some,,given,,termsThree-digit,,numbers,,not,,divisible,,by,,3Binomial,,TheoremSystem,,of,,EquationsVariation,,/,,ProportionalVerbal,,Problems,,in,,Algebra,,Matched,,Content,,Hello,,Guest,,�,,Please,,Login,,�,,Or,,Register,,�,,OrLogin,,With,,Facebook,,,,Like,,us,,on,,Facebook,,SPONSORED,,LINKS,,Recent,,Reviewer,,Updates,,Problem,,432,,-,,Force,,in,,Members,,of,,a,,Truss,,by,,Method,,of,,Sections,,Problem,,431,,-,,Members,,in,,the,,Third,,Panel,,of,,a,,Parker,,Truss,,Problem,,430,,-,,Parker,,Truss,,by,,Method,,of,,Sections,,Problem,,429,,-,,Cantilever,,Truss,,by,,Method,,of,,Sections,,03,,Excess,,of,,the,,Sum,,of,,Parts,,over,,the,,Difference,,of,,Parts,,of,,a,,Number,,02,,-,,Time,,for,,the,,thermometer,,reading,,to,,drop,,to,,within,,half,,degree,,of,,the,,air,,temperature,,Problem,,428,,-,,Howe,,Truss,,by,,Method,,of,,Sections,,Problem,,427,,-,,Interior,,Members,,of,,Nacelle,,Truss,,by,,Method,,of,,Sections,,Problem,,426,,-,,Fink,,Truss,,by,,Method,,of,,Sections,,Problem,,425,,-,,Fink,,Truss,,by,,Method,,of,,Sections,,Active,,Forum,,Topics,,Discussion,,on:,,Solution,,to,,Problem,,225,,Biaxial,,DeformationCONDITIONAL,,STATEMENT,,C PhysicsPlease,,help,,me,,to,,graph,,this,,polar,,equationtime,,raTEBernoulis,,normal,,stressesCentroids,,and,,Centers,,of,,Gravity;,,Moments,,of,,InertiaPhysicsSolid,,geometryMore,,Reviewer,,by,,MATHalino.com,,Algebra,,Trigonometry,,Spherical,,Trigonometry,,Plane,,Geometry,,Solid,,Mensuration,,Analytic,,Geometry,,Differential,,Calculus,,Integral,,Calculus,,Differential,,Equations,,Advance,,Math,,Engineering,,Mechanics,,Strength,,of,,Materials,,Engineering,,Economy,,.,,The,,,reason,,,is,,,that,,,,necessarily,,,,at,,,least,,,one,,,denominator,,,of,,,the,,,progression,,,will,,,be,,,divisible,,,by,,,a,,,prime,,,number,,,that,,,does,,,not,,,divide,,,any,,,other,,,denominator.[1].,,,You,,can,,help,,Wikipedia,,by,,expanding,,it.,,The,,,common,,,difference,,,of,,,the,,,above,,,AP,,,is,,,d,,,=,,,8,,,-,,,3,,,=,,,13,,,-,,,8,,,=,,,.,,,Example,of,geometric,progression,is,,1,,3,,9,,27,,.,Notes,,,,formulas,,,and,,,solved,,,problems.,,,Quizzes,,on,,ProgressionsMCQ,,#1:,,Arithmetic,,ProgressionMCQ,,#2:,,Geometric,,ProgressionMCQ,,#3,,:,,More,,on,,Geometric,,Progressions.MCQ,,#4,,:,,Harmonic,,Progressions.MCQ,,#5:,,More,,on,,Harmonic,,ProgressionMCQ,,#6:,,Mixed,,ProgressionsComplex,,NumbersMCQ,,#1MCQ,,#2:,,More,,on,,Complex,,NumbersQuadratic,,EquationsMCQ,,Quadratic,,EquationsQuadratic,,In-equationsMCQ,,Quadratic,,In-equationsCoordinate,,Geometry,,-,,Straight,,LinesMCQ,,#1:,,Cartesian,,Planes,,,Straight,,Line,,BasicsMCQ,,#2,,on,,Straight,,LinesMCQ,,#3,,on,,Straight,,LinesMCQ,,#4,,on,,Straight,,LinesCircles1MCQ,,#1,,on,,Circles.2MCQ,,#2,,on,,Circles.3MCQ,,#3,,on,,Circles.Conic,,Sections-,,Parabola,,,Hyperbola,,,Ellipse1MCQ-,,The,,Basics,,of,,Conic,,Sections2MCQ,,on,,Parabola.3MCQ,,on,,Hyperbola4MCQ,,on,,Ellipses.ProbabilityMCQ,,#1,,on,,Basic,,ProbabilityMCQ,,#2:,,More,,Challenging,,Problems,,on,,ProbabilityMCQ,,#3-,,Conditional,,Probability,,and,,Bayes,,TheoremSeries,,and,,Progressions,,:,,AP,,,GP,,,HPAfter,,studying,,the,,chapter,,you,,might,,find,,it,,useful,,to,,attempt,,these,,Multiple,,Choice,,Question,,Quizzes,,to,,assess,,how,,well,,you,,understood,,the,,topic.MCQ,,Quiz#1MCQ,,Quiz/Worksheet,,#2MCQ,,Quiz/Worksheet,,#3MCQ,,Quiz/Worksheet,,#4MCQ,,Quiz/Worksheet,,#5MCQ,,Quiz/Worksheet,,#6A,,sequence,,refers,,to,,a,,list,,of,,numbers,,with,,some,,inherent,,pattern.General,,term,,of,,a,,sequence,,,generally,,written,,as,,an,,is,,an,,expression,,that,,for,,different,,values,,ofn,,gives,,different,,terms,,of,,the,,sequence.Arithmetic,,Progression,,,Terms,,and,,SummationA,,sequence,,of,,the,,typea,a d,a 2d,a 3d,is,,said,,to,,form,,an,,AP.Each,,term,,differs,,from,,the,,previous,,one,,by,,a,,fixed,,value,,called,,as,,common,,difference.a,,and,,d,,are,,usually,,used,,to,,denote,,first,,term,,and,,common,,difference,,respectively.nth,,term,,of,,an,,AP,,is,,given,,byan=a1 (n-1)dThe,,tutorial,,will,,show,,you,,how,,to,,compute,,the,,sum,,of,,the,,first,,n,,terms,,of,,an,,APSelecting,,terms,,in,,AP:3,,terms,,in,,an,,AP,,are,,,,a-d,a,a d4,,terms,,in,,an,,AP,,are,,,,a-3d,a-d,a d,a 3dAnd,,so,,on.mth,,term,,from,,the,,end,,of,,an,,AP,,:It,,is,,the,,(n-m 1)th,,term,,from,,the,,beginning.Alternately,,,we,,can,,reverse,,the,,AP,,,and,,consider,,the,,first,,term,,and,,common,,difference,,of,,thenew,,AP,,as,,last,,term,,and,,negative,,of,,common,,difference,,of,,the,,old,,AP.If,,a,,constant,,is,,added,,,or,,subtracted,,,or,,multiplied,,or,,divided,,from,,every,,term,,on,,an,,AP,,,theresulting,,sequence,,is,,still,,an,,AP.Arithmetic,,Mean:if,,a,b,c,,are,,in,,AP,,,then,,b,,is,,said,,to,,be,,arithmetic,,mean,,of,,a,,and,,c.Equivalently,,,if,,2b=a c,,,then,,a,b,c,,are,,in,,AP.If,,between,,a,,and,,b,,we,,are,,to,,insert,,n,,numbers,,A1,A2,A3,.,An,,such,,that,,a,,,A1,A2,A3,.,An,,form,,anAP,,,then,,A1,A2,A3,.,An,,are,,called,,n,,Arithmetic,,Means.Geometric,,Progression,,,Terms,,and,,SummationA,,sequence,,of,,the,,type:a,ar,ar2,ar3,is,,called,,a,,GP.In,,a,,GP,,,thenth,,term,,of,,a,,GP,,is,,given,,by:an=arm-1The,,tutorial,,will,,show,,you,,how,,to,,compute,,the,,sum,,of,,first,,n,,terms,,of,,a,,GP.When,,r=1,,,the,,GP,,can,,be,,treated,,as,,an,,AP,,,and,,clearly,,the,,sum,,of,,first,,n,,terms,,then,,is,,nXa.Similar,,to,,an,,AP,,,mth,,term,,from,,the,,end,,is,,(n-m 1)th,,term,,from,,the,,starting.Selecting,,terms,,in,,a,,GP:A,,GP,,of,,3,,terms,,:,,a/r,a,arA,,GP,,of,,4,,terms:a/r3,a/r,ar,ar3And,,so,,on.If,,all,,terms,,in,,a,,GP,,are,,multiplied,,or,,divided,,by,,the,,same,,number,,,or,,are,,raised,,to,,the,,samepower,,,then,,the,,resulting,,sequence,,is,,still,,a,,GP.Geometric,,Mean:If,,a,b,c,,are,,in,,GP,,then,,b2=ac,,and,,b,,is,,called,,the,,GM,,of,,a,,and,,c.Conversely,,,if,,b2=ac,,,then,,a,b,c,,are,,in,,GP.Sum,,of,,infinite,,terms,,of,,a,,GP:If,,-1,,GM>HMHere,,are,,some,,of,,the,,problems,,solved,,in,,the,,tutorial,,:Q:,,What,,is,,the,,common,,difference,,of,,an,,AP,,whose,,nth,,term,,is,,xn y?Q:,,If,,the,,sum,,of,,n,,terms,,of,,an,,AP,,is,,2n2 3n,,,what,,is,,the,,kth,,term?Q:If,,am=n,,and,,an=m,,,what,,is,,ap?Q:If,,the,,sums,,of,,n,,terms,,of,,two,,arithmetic,,progressions,,are,,in,,the,,ratio,,2n 5:3n 4,,,then,,what,,is,,theratio,,of,,their,,nth,,terms?Q:,,If,,sum,,of,,n,,terms,,of,,an,,AP,,is,,3n2 5n,,then,,which,,of,,its,,terms,,is,,164?Q:,,If,,sum,,of,,first,,p,,terms,,is,,q,,and,,sum,,of,,first,,q,,terms,,is,,p,,then,,what,,is,,the,,sum,,of,,first,,p q,,terms,,?Q:,,If,,four,,numbers,,are,,in,,AP,,such,,that,,their,,sum,,is,,50,,,and,,the,,greatest,,number,,is,,four,,times,,the,,least,then,,what,,are,,the,,numbers?Q:,,If,,n,,arithmetic,,means,,are,,inserted,,between,,1,,and,,31,,such,,that,,ratio,,of,,first,,and,,nth,,mean,,is,,3:29,then,,what,,is,,the,,value,,of,,n?Q:,,If,,S1,,is,,the,,sum,,of,,an,,AP,,of,,n,,odd,,number,,of,,terms,,and,,S2,,the,,sum,,of,,terms,,of,,the,,series,,in,,oddplaces,,,then,,what,,is,,S1/S2?Q:,,What,,is,,the,,sum,,of,,2,,digit,,multiples,,of,,4?Q:,,Find,,the,,sum,,of,,2 6 18 4374.Q:,,Find,,the,,sum,,of,,5 55 555 n,,termsQ:,,Find,,the,,sum,,of,,n,,terms,,of,,the,,sequence,,whose,,nth,,term,,is,,2n 3nQ:,,Find,,a,,GP,,for,,which,,the,,sum,,of,,first,,two,,terms,,is,,-4,,and,,the,,fifth,,term,,is,,4,,times,,the,,third,,term.Q:,,Find,,the,,least,,value,,of,,n,,for,,which,,the,,sum,,of,,1 3 9 27 ,,to,,n,,terms,,is,,greater,,than,,7000.Q:,,If,,a,b,c,,are,,in,,GP,,,prove,,that,,log,,a,,,log,,b,,,log,,c,,are,,in,,AP,,and,,vice,,versa.Q:,,If,,a,b,c,,are,,in,,GP,,and,,x,y,,are,,AMs,,between,,a,b,,and,,b,c,,respectively,,,then,,prove,,that,,x,b,y,,are,,inHP.Q:,,Find,,the,,sum,,to,,n,,terms,,of,,series1.2.3 2.3.4 3.4.5 4.5.6 Q:If,,a,,,b,,,c,,are,,in,,H.P.,,,show,,that,,a/b c,,,b/c a,,,c/a b,,are,,also,,in,,H.P.Q:Evaluate:,,62,, ,,72,, ,,82,, ,,92,, ,,102Q:,,Prove,,that,,(a,, ,,b,, ,,c),,(ab,, ,,bc,, ,,ca),,>,,9abc.Q:,,If,,a2,,,b2,,,c2,,are,,in,,A.P.,,Notes,,formulas,and,solved,problems,related,to,these,sub-topics.The,Principle,of,Mathematical,InductionIntroductory,problems,related,to,Mathematical,Induction.Quadratic,EquationsIntroducing,various,techniques,by,which,quadratic,equations,can,be,solved,-,factorization,,direct,formula.,Lapok,,,(in,,,Hungarian),,,,39:,,,1724.,,,Relationship,,,between,,,roots,,,of,,,a,,,quadratic,,,equation.,,,Soc.,,,Budapest,,,pp.289309,,,doi:10.1007/978-3-642-39286-39,,,MR3203600.,,,Example,2:,5,,2,,-1,,.,,,which,,is,,an,,AP,,with,,a,,common,,difference,,of,,3.,,Contents,,,1,,,Examples,,,2,,,Use,,,in,,,geometry,,,3,,,See,,,also,,,4,,,References,,,.,,,2,,MCQ,,#2,,on,,Circles.,, 5d80d7912b

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