Sequence and Series questions
1035 published questions with worked solutions.
- If the sum of series 1 1 (1+d) + 1 (1+d)(1+2d) + + 1 (1+9d)(1+10d) is equal to 5, then 50d is equal to
- The 20ᵗʰ term from the end of the progression 20, 19 14, 18 12, 17 34, , -129 14 is :
- The number of common terms in the progressions 4, 9, 14, 19, ......, upto 25th term and 3, 6, 9, 12, ......, upto 37th term is :
- If each term of a geometric progression a₁, a₂, a₃, ..... with a₁ = 1/8 and a₂ ≠ a₁, is arithmetic mean of the next two terms,...
- In an A.P., the sixth term a₆ = 2. If the product a₁a₄a₅ is the greatest, then the common difference of the A.P. is equal to
- If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P. then the common ratio of the...
- Let a and b be two distinct real numbers. Let 11ᵗʰ term of a GP, whose first term is a and third term is b, is equal to pᵗʰ term...
- Let Sₙ be the sum to n-terms of an arithmetic progression 3, 7, 11, ...... . If 40 < ( 6 n(n+1) _ k=1 ^nS_k ) < 42, then n equals...
- Let Sₙ denote the sum of first n terms of an arithmetic progression. If S₂₀ = 790 and S₁₀ = 145, then S₁₅ – S₅ is:
- Let 2ⁿᵈ, 8ᵗʰ and 44ᵗʰ terms of a non-constant A.P. be respectively the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ terms of a G.P. If the first term of the...
- The sum of the series 1 1 - 3 1^2 + 1^4 + 2 1 - 3 2^2 + 2^4 + 3 1 - 3 3^2 + 3^4 + up to 10-terms is
- Let S_n=1 (n-1)+2 (n-2)+3 (n-3)+ +(n-1) 1, n 4. The sum _ n=4 ^ ( 2S_n n! - 1 (n-2)! ) is equal to :
- Let a_1, a_2,......,a_ 21 be an AP such that _ n=1 ^ 20 1 a_na_ n+1 = 4 9 . If the sum of this AP is 189, then a_6a_ 16 is equal...
- Let 1 16 , a and b be in G.P. and 1 a , 1 b , 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ________.
- Consider an arithmetic series and a geometric series having four initial terms from the set 11, 8, 21, 16, 26, 32, 4 . If the...
- If 1, _ 10 (4^x-2) and _ 10 (4^x+ 18 5 ) are in arithmetic progression for a real number x, then the value of the determinant...
- Let S_1 be the sum of first 2n terms of an arithmetic progression. Let S_2 be the sum of first 4n terms of the same arithmetic...
- If _ r=1 ^ 10 r!(r^3+6r^2+2r+5)= (11!), then the value of is equal to _________.
- Let a_n _ n=1 ^ be a sequence such that a_1 = 1, a_2 = 1 and a_ n+2 =2a_ n+1 +a_n for all n 1. Then the value of 47 _ n=1 ^ a_n...
- Let S_n denote the sum of first n-terms of an arithmetic progression. If S_ 10 = 530, S_5 = 140, then S_ 20 -S_6 is equal to :
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