Algebra · Chapter 14 of 20
Sequences & series
165 curated · 313 from open sources · 14.3 million generated
Practice
14.3 millionEndless problems made on demand, each with an exactly computed answer. Every click is a new one.
Curated
165| # | Title | Difficulty | Source | Tags | |
|---|---|---|---|---|---|
| 12 | Integer echoesRecurrences | Medium | Lemma | ||
| 45 | A third at a timeSums | Medium | Lemma | ||
| 813 | Arithmetic means between fractionsSequences & series | Medium | Hall & Knight | ||
| 814 | Arithmetic means between mixed numbersSequences & series | Medium | Hall & Knight | ||
| 815 | Arithmetic means with variable termSequences & series | Medium | Hall & Knight | ||
| 821 | Three numbers in APSequences & series | Medium | Hall & Knight | ||
| 822 | Numbers from sum of cubesSequences & series | Medium | Hall & Knight | ||
| 826 | Sum of mixed quadratic seriesSequences & series | Medium | Hall & Knight | ||
| 830 | First term and lengthSequences & series | Medium | Hall & Knight | ||
| 831 | First term and length from later termsSequences & series | Medium | Hall & Knight | ||
| 832 | First installment of a debt repaymentSequences & series | Medium | Hall & Knight | ||
| 833 | Number of arithmetic meansSequences & series | Medium | Hall & Knight | ||
| 835 | Sum of mixed seriesSequences & series | Medium | Hall & Knight | ||
| 836 | Sum of n termsSequences & series | Medium | Hall & Knight | ||
| 837 | Relation among three termsSequences & series | Medium | Hall & Knight | ||
| 838 | Sum of p+q termsSequences & series | Medium | Hall & Knight | ||
| 839 | Four integers in A.P.Sequences & series | Medium | Hall & Knight | ||
| 840 | Divide 20 into A.P.Sequences & series | Medium | Hall & Knight | ||
| 841 | Term swapping in A.P.Sequences & series | Medium | Hall & Knight | ||
| 843 | General term from sum formulaSequences & series | Medium | Hall & Knight | ||
| 846 | Number of terms from partial sumsSequences & series | Medium | Hall & Knight | ||
| 847 | Relation for equal meansSequences & series | Medium | Hall & Knight | ||
| 952 | Third ProportionalSequences & series | Medium | Hall & Knight | ||
| 953 | Proportion Identity Proof OneSequences & series | Medium | Hall & Knight | ||
| 954 | Proportion Identity Proof TwoSequences & series | Medium | Hall & Knight | ||
| 955 | Proportion Identity Proof ThreeSequences & series | Medium | Hall & Knight | ||
| 968 | Four proportionals with given sumsSequences & series | Medium | Hall & Knight | ||
| 969 | Mixing sherry from two casksSequences & series | Medium | Hall & Knight | ||
| 970 | Capacity of a wine cask after two dilutionsSequences & series | Medium | Hall & Knight | ||
| 972 | Town versus country population in 1871Sequences & series | Medium | Hall & Knight | ||
| 973 | Comparing percentage increases of tea and coffeeSequences & series | Medium | Hall & Knight | ||
| 993 | Diamond and Gold Ring ValuesSequences & series | Medium | Hall & Knight | ||
| 1004 | Sum of alternating geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1006 | Insert geometric meansSequences & series | Medium | Hall & Knight | ||
| 1007 | Inserting Geometric MeansSequences & series | Medium | Hall & Knight | ||
| 1013 | Sum of a geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1014 | Common ratio from partial sumsSequences & series | Medium | Hall & Knight | ||
| 1015 | Determine the GP from two termsSequences & series | Medium | Hall & Knight | ||
| 1016 | First term from sum and last termSequences & series | Medium | Hall & Knight | ||
| 1017 | Common ratio from first, last and sumSequences & series | Medium | Hall & Knight | ||
| 1018 | Three numbers in GP from sum and productSequences & series | Medium | Hall & Knight | ||
| 1019 | Three numbers in geometric progressionSequences & series | Medium | Hall & Knight | ||
| 1020 | Relation between geometric series sumsSequences & series | Medium | Hall & Knight | ||
| 1021 | Exponential relation of GP termsSequences & series | Medium | Hall & Knight | ||
| 1029 | Compare terms of two progressionsSequences & series | Medium | Hall & Knight | ||
| 1030 | Sum of geometric series equalitySequences & series | Medium | Hall & Knight | ||
| 1031 | Sum of complicated infinite seriesSequences & series | Medium | Hall & Knight | ||
| 1032 | Three numbers in geometric progressionSequences & series | Medium | Hall & Knight | ||
| 1033 | Sum of a combined seriesSequences & series | Medium | Hall & Knight | ||
| 1034 | Sum of mixed geometric termsSequences & series | Medium | Hall & Knight | ||
| 1035 | Alternating arithmetic‑geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1038 | Relation among four consecutive G.P. termsSequences & series | Medium | Hall & Knight | ||
| 1039 | Arithmetic and geometric mean conditionSequences & series | Medium | Hall & Knight | ||
| 1040 | Sum of arithmetico-geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1041 | Alternating ratio seriesSequences & series | Medium | Hall & Knight | ||
| 1042 | Sum of partial sums of GPSequences & series | Medium | Hall & Knight | ||
| 1043 | Sum of infinite geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1047 | Numbers with given meansSequences & series | Medium | Hall & Knight | ||
| 1049 | Proportion in harmonic progressionSequences & series | Medium | Hall & Knight | ||
| 1050 | Harmonical Progression PropertySequences & series | Medium | Hall & Knight | ||
| 1051 | Terms of a Harmonical ProgressionSequences & series | Medium | Hall & Knight | ||
| 1056 | Sum of a cubic‑quadratic seriesSequences & series | Medium | Hall & Knight | ||
| 1057 | Sum of exponential differenceSequences & series | Medium | Hall & Knight | ||
| 1061 | Nth term from quadratic sumSequences & series | Medium | Hall & Knight | ||
| 1063 | Means ratio identitySequences & series | Medium | Hall & Knight | ||
| 1067 | Rectangular pyramidal cannonballsSequences & series | Medium | Hall & Knight | ||
| 1068 | Incomplete triangular pyramidSequences & series | Medium | Hall & Knight | ||
| 1069 | Incomplete square pyramid with given coursesSequences & series | Medium | Hall & Knight | ||
| 1070 | Find length from rectangular pyramid totalSequences & series | Medium | Hall & Knight | ||
| 1071 | Shot count in square pileSequences & series | Medium | Hall & Knight | ||
| 1072 | Complete rectangular pileSequences & series | Medium | Hall & Knight | ||
| 1073 | Incomplete rectangular pileSequences & series | Medium | Hall & Knight | ||
| 1074 | Complete rectangular pile from topSequences & series | Medium | Hall & Knight | ||
| 1075 | Triangular vs square pileSequences & series | Medium | Hall & Knight | ||
| 1076 | Incomplete square pileSequences & series | Medium | Hall & Knight | ||
| 1077 | Shot count in square vs triangular pileSequences & series | Medium | Hall & Knight | ||
| 1078 | Shot numbers from given ratioSequences & series | Medium | Hall & Knight | ||
| 1079 | Lowest layer of a triangular shot pileSequences & series | Medium | Hall & Knight | ||
| 1080 | Remaining shot forms a triangular pileSequences & series | Medium | Hall & Knight | ||
| 1387 | Binomial Expansion with Negative PowersSequences & series | Medium | Hall & Knight | ||
| 1397 | Fifth term with fractional powersSequences & series | Medium | Hall & Knight | ||
| 1399 | Difference of fifth powersSequences & series | Medium | Hall & Knight | ||
| 1400 | Difference of sixth powers with radicalsSequences & series | Medium | Hall & Knight | ||
| 1401 | Sum of sixth powers with a variableSequences & series | Medium | Hall & Knight | ||
| 1408 | Coefficient of x to the rSequences & series | Medium | Hall & Knight | ||
| 1409 | Term Independent for MultiplesSequences & series | Medium | Hall & Knight | ||
| 1410 | Coefficient of x to the pSequences & series | Medium | Hall & Knight | ||
| 1423 | Term from the EndSequences & series | Medium | Hall & Knight | ||
| 1425 | Relation Between IndicesSequences & series | Medium | Hall & Knight | ||
| 1426 | Middle Term of BinomialSequences & series | Medium | Hall & Knight | ||
| 1428 | Sum of Weighted Coefficients IISequences & series | Medium | Hall & Knight | ||
| 1443 | Binomial expansion with leading constantSequences & series | Medium | Hall & Knight | ||
| 1444 | Binomial expansion with square root of a constantSequences & series | Medium | Hall & Knight | ||
| 1446 | Binomial Expansion with Negative CoefficientSequences & series | Medium | Hall & Knight | ||
| 1449 | Specific Term with Higher PowerSequences & series | Medium | Hall & Knight | ||
| 1450 | Specific Term of Rational PowerSequences & series | Medium | Hall & Knight | ||
| 1453 | Specific term of scaled binomial powerSequences & series | Medium | Hall & Knight | ||
| 1454 | Seventh term of binomial expansionSequences & series | Medium | Hall & Knight | ||
| 1459 | Greatest term in binomial expansionSequences & series | Medium | Hall & Knight | ||
| 1460 | Greatest term in fractional binomial expansionSequences & series | Medium | Hall & Knight | ||
| 1461 | Greatest term in negative fractional binomialSequences & series | Medium | Hall & Knight | ||
| 1462 | Greatest term with two variablesSequences & series | Medium | Hall & Knight | ||
| 1463 | Two equal greatest terms in binomial expansionSequences & series | Medium | Hall & Knight | ||
| 1468 | Fourth root approximationSequences & series | Medium | Hall & Knight | ||
| 1469 | Reciprocal cube rootSequences & series | Medium | Hall & Knight | ||
| 1470 | Fractional power approximationSequences & series | Medium | Hall & Knight | ||
| 1477 | Approximation with Small QuantitiesSequences & series | Medium | Hall & Knight | ||
| 1478 | Fractional ApproximationSequences & series | Medium | Hall & Knight | ||
| 1479 | Coefficient in Negative Power ExpansionSequences & series | Medium | Hall & Knight | ||
| 1481 | First Three Terms of ProductSequences & series | Medium | Hall & Knight | ||
| 1482 | First Three Terms of Rational CombinationSequences & series | Medium | Hall & Knight | ||
| 1483 | Binomial coefficient relationSequences & series | Medium | Hall & Knight | ||
| 1486 | General coefficient of rational fractionSequences & series | Medium | Hall & Knight | ||
| 1487 | General coefficient with cubic factorSequences & series | Medium | Hall & Knight | ||
| 1488 | Prove an infinite series identitySequences & series | Medium | Hall & Knight | ||
| 1489 | Prove a root series identitySequences & series | Medium | Hall & Knight | ||
| 1490 | Binomial Series Identity TransformationSequences & series | Medium | Hall & Knight | ||
| 1491 | Equivalence of Binomial SeriesSequences & series | Medium | Hall & Knight | ||
| 1492 | Approximate Expansion of FunctionSequences & series | Medium | Hall & Knight | ||
| 1493 | Parity of Surd Power Integer PartSequences & series | Medium | Hall & Knight | ||
| 1494 | Parity of Another Surd PowerSequences & series | Medium | Hall & Knight | ||
| 1495 | Coefficient in Reciprocal SeriesSequences & series | Medium | Hall & Knight | ||
| 1500 | Sum of Products of Binomial CoefficientsSequences & series | Medium | Hall & Knight | ||
| 1502 | Alternating Harmonic Series of Binomial CoefficientsSequences & series | Medium | Hall & Knight | ||
| 1534 | Sum of Natural Numbers Series ExpansionSequences & series | Medium | Hall & Knight | ||
| 1550 | Coefficient in multinomial expansionSequences & series | Medium | Hall & Knight | ||
| 1551 | Coefficient of high powerSequences & series | Medium | Hall & Knight | ||
| 1552 | Coefficient from rational expressionSequences & series | Medium | Hall & Knight | ||
| 1554 | Power series expansion up to quintic termSequences & series | Medium | Hall & Knight | ||
| 1555 | Series expansion with constant multiplierSequences & series | Medium | Hall & Knight | ||
| 1630 | Amount of an AnnuitySequences & series | Medium | Hall & Knight | ||
| 1634 | Amount of Annuity for Two YearsSequences & series | Medium | Hall & Knight | ||
| 1635 | Perpetual and Term AnnuitiesSequences & series | Medium | Hall & Knight | ||
| 1636 | Deferred Freehold EstateSequences & series | Medium | Hall & Knight | ||
| 1639 | Repayment by InstalmentsSequences & series | Medium | Hall & Knight | ||
| 1641 | Renewing a LeaseSequences & series | Medium | Hall & Knight | ||
| 1643 | Perpetual Increasing AnnuitySequences & series | Medium | Hall & Knight | ||
| 1717 | Sum of odd squaresSequences & series | Medium | Hall & Knight | ||
| 1718 | Sum of consecutive productsSequences & series | Medium | Hall & Knight | ||
| 1719 | Sum of mixed productsSequences & series | Medium | Hall & Knight | ||
| 1720 | Sum of odd cubesSequences & series | Medium | Hall & Knight | ||
| 1721 | Sum of fourth powersSequences & series | Medium | Hall & Knight | ||
| 1732 | Determine Parameters for a General TermSequences & series | Medium | Hall & Knight | ||
| 1733 | Coefficients in Rational ExpansionSequences & series | Medium | Hall & Knight | ||
| 1734 | Series Expansion of Implicit FunctionSequences & series | Medium | Hall & Knight | ||
| 1748 | General Term of ExpandoSequences & series | Medium | Hall & Knight | ||
| 1749 | General Term of Partial FractionsSequences & series | Medium | Hall & Knight | ||
| 1750 | General Term of Rational FunctionSequences & series | Medium | Hall & Knight | ||
| 1753 | General term with repeated factorSequences & series | Medium | Hall & Knight | ||
| 1754 | General term of three linear factorsSequences & series | Medium | Hall & Knight | ||
| 1756 | Sum of infinite alternating power seriesSequences & series | Medium | Hall & Knight | ||
| 1759 | Generating function with alternating signsSequences & series | Medium | Hall & Knight | ||
| 1760 | Generating function of an exponential-like seriesSequences & series | Medium | Hall & Knight | ||
| 1763 | Sum of a recurring seriesSequences & series | Medium | Hall & Knight | ||
| 1764 | Recurring series term and sumSequences & series | Medium | Hall & Knight | ||
| 1766 | Alternate recurring seriesSequences & series | Medium | Hall & Knight | ||
| 1767 | Scales of relation for powersSequences & series | Medium | Hall & Knight | ||
| 1768 | Sum of recurring series from infinitySequences & series | Medium | Hall & Knight | ||
| 1769 | Sum of a complex seriesSequences & series | Medium | Hall & Knight | ||
| 1887 | Finite Series Identity OneSequences & series | Medium | Hall & Knight | ||
| 1888 | Finite Series Identity TwoSequences & series | Medium | Hall & Knight | ||
| 1889 | Finite Series Identity ThreeSequences & series | Medium | Hall & Knight | ||
| 1890 | Finite Series Identity FourSequences & series | Medium | Hall & Knight | ||
| 1891 | Sum of series with telescoping terms ISequences & series | Medium | Hall & Knight | ||
| 1905 | Deciphering the ManuscriptSequences & series | Medium | Hall & Knight |
From open sources
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