Sequence and Series questions
1035 published questions with worked solutions.
- Let A_ 1 , A_ 2 , A_ 3 , ... be an increasing geometric progression of positive real numbers. If A_ 1 A_ 3 A_ 5 A_ 7 = 1/1296 and...
- Let a_ n _ n=0 ^ be a sequence such that a_ 0 = a_ 1 = 0 and a_ n+2 = 3a_ n+1 - 2a_ n + 1, ∀ n 0. Then a_ 25 a_ 23 - 2a_ 25 a_ 22...
- Let a_ 1 , a_ 2 , a_ 3 , _____ be an A.P. If _ r=1 ^ a_ r /2^ r = 4, then 4a_ 2 is equal to _____.
- If 1/(2 3 4) + 1/(3 4 5) + 1/(4 5 6) + … + 1/(100 101 102) = k/101, then 34k is equal to _____.
- Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the...
- Let a_ n _ n=0 ^ be a sequence such that a_ 0 = a_ 1 = 0 and a_ n+2 = 2a_ n+1 - a_ n + 1 for all n 0. Then _ n=2 ^ a_ n /7^ n is...
- The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of
- The sum of (p+q)^ th and (p-q)^ th terms of an AP is equal to
- What is the fourth term of an AP of n terms whose sum is n(n+1)?
- The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + … is
- Let a_1,a_2,a_3,….,a_n be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then _ n...
- Let a_n be n^ th term of the series 5 + 8 + 14 + 23 + 35 + 50 + ......... and S_n= _ k=1 ^na_k. Then S_ 30 -a_ 40 is equal to
- Let 0<z<y<x be three real numbers such that 1 x , 1 y , 1 z are in an arithmetic progression and x, 2y, z are in a geometric...
- Let _ j=1 ^nS_j^2= n A (Bn^2+Cn+D), where A, B, C, D N and A has least value. Then
- Suppose a_1, a_2, 2, a_3, a_4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric...
- Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first...
- The sum of all those terms, of the arithmetic progression 3, 8, 13,……, 373, that are not divisible by 3, is equal to _________
- For k N, if the sum of the series 1+ 4 k + 8 k^2 + 13 k^3 + 19 k^4 + is 10, then the value of k is .........
- Let x_1, x_2, …, x_ 100 be in an arithmetic progression, with x_1 = 2 and their mean equal to 200. If y_i=i(x_i-i), 1 100, then...
- Let S = 109 + 108 5 + 107 5^2 + + 2 5^ 107 + 1 5^ 108 . Then the value of 16S-(25)^ -54 is equal to _________.
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration