Sequence and Series questions
1035 published questions with worked solutions.
- Let the sum of the first n terms of a non-constant A.P., a_1, a_2, a_3, be 50n + n(n-7) 2 A, where A is a constant. If d is the...
- The sum 1 + 1^3+2^3 1+2 + 1^3+2^3+3^3 1+2+3 + + 1^3+2^3+3^3+ +15^3 1+2+3+ +15 - 1 2 (1+2+3+ +15) is equal to:
- If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval
- If x_1, x_2, , x_n and 1 h_1 , 1 h_2 , , 1 h_n are two A.P's such that x_3 = h_2 = 8 and x_8 = h_7 = 20, then x_5 h_ 10 equals
- Let A_n = ( 3 4 ) - ( 3 4 )^2 + ( 3 4 )^3 - + (-1)^ n-1 ( 3 4 )^n and B_n = 1 - A_n. Then, the least odd natural number p, so...
- If a, b, c are in A.P. and a^2, b^2, c^2 are in G.P. such that a < b < c and a + b + c = 3 4 , then the value of a is -
- The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + .... up to 11th term is:
- If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is:
- The sum 3 1^3 1^2 + 5 (1^3 + 2^3) 1^2 + 2^2 + 7 (1^3 + 2^3 + 3^3) 1^2 + 2^2 + 3^2 + up to 10th term is:
- If a_1, a_2, a_3, , a_n are in A.P. and a_1 + a_4 + a_7 + + a_ 16 = 114, then a_1 + a_6 + a_ 11 + a_ 16 is equal to:
- The sum of the following series 1 + 6 + 9(1^2 + 2^2 + 3^2) 7 + 12(1^2 + 2^2 + 3^2 + 4^2) 9 + 15(1^2 + 2^2 + + 5^2) 11 + up to 15...
- Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the three consecutive terms...
- If a, b and c be three distinct real numbers in G.P. and a + b + c = xb, then x cannot be:
- Let a_1, a_2, , a_ 30 be an A.P., S = _ i=1 ^ 30 a_i and T = _ i=1 ^ 15 a_ (2i-1) . If a_5 = 27 and S − 2T = 75, then a_ 10 is...
- If α and β are the roots of the equation 375x^2 - 25x - 2 = 0, then _ n _ r=1 ^n ^r + _ n _ r=1 ^n ^r is equal to:
- Let S_n denote the sum of the first n terms of an A.P. If S_4 = 16 and S_6 = -48, then S_ 10 is equal to:
- If the sum of the first 15 terms of the series ( 34 )^3 + (1 12 )^3 + (2 14 )^3 + 3^3 + (3 34 )^3 + is equal to 225k, then k is...
- If ^nC_4, ^nC_5 and ^nC_6 are in A.P., then n can be:
- Let S_k = 1 + 2 + 3 + + k k . If S_1^2 + S_2^2 + + S_ 10 ^2 = 5 12 A, then A is equal to:
- The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the...
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