Sequence and Series questions
1035 published questions with worked solutions.
- The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ...., is -
- If x, y, z are in A.P. and ^ -1 x, ^ -1 y and ^ -1 z are also in A.P., then -
- Let a_1, a_2, a_3, be a G.P. of increasing positive terms such that a_2 a_3 a_4 = 64 and a_1 + a_3 + a_5 = 813 7 . Then a_3 + a_5...
- Let a_1 = 1 and for n 1, a_ n+1 = 1 2 a_n + n^2 - 2n - 1 n^2(n+1)^2 . Then | _ n=1 ^ (a_n - 2 n^2 ) | is equal to
- Let a_1, a_2 2 , a_3 2^2 , , a_ 10 2^9 be a G.P. of common ratio 1 2 . If a_1 + a_2 + + a_ 10 = 62, then a_1 is equal to:
- If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve...
- Suppose a,b,c are in A.P. and a^2, 2b^2, c^2 are in G.P. If a<b<c and a+b+c=1, then 9(a^2+b^2+c^2) is equal to ____ .
- Let _ k=1 ^ n a_k = n^2 + n. If a_ 10 = 59 and a_6 = 7a_1 then + is equal to
- Let 729, 81, 9, 1, be a sequence and P_n denote the product of the first n terms of this sequence. If 2 _ n=1 ^ 40 (P_n)^ 1 n =...
- Consider an A.P.: a_1, a_2, , a_n; a_1>0. If a_2 - a_1 = -3 4 , a_n = 1 4 a_1, and _ i=1 ^ n a_i = 525 2 , then _ i=1 ^ 17 a_i is...
- Let _1, _2, _3, _4 be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If _1+ _2+...
- ( 1 3 + 4 7 )+ ( 1 3^2 + 1 3 4 7 + 4^2 7^2 )+ ( 1 3^3 + 1 3^2 4 7 + 1 3 4^2 7^2 + 4^3 7^3 )+ upto infinite terms is equal to -
- The common difference of the A.P.: a_1,a_2, ,a_m is 13 more than the common difference of the A.P.: b_1,b_2, ,b_n. If b_ 31 =...
- In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms...
- 6 3^ 26 + 10.1 3^ 25 + 10.2 3^ 24 + 10.2^2 3^ 23 + + 10.2^ 24 3 is equal to
- Let a1, a2, a3..... be a G.P. of increasing positive terms. If a1a5 = 28 and a2 + a4 = 29, then a6 is equal to
- Suppose that the number of terms in an A.P is 2k, k N. If the sum of all odd terms of the A.P. is 40, the sum of all even terms...
- The roots of the quadratic equation 3x^2 – px + q = 0 are 10th and 11th terms of an arithmetic progression with common difference...
- If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms,...
- Let S_n = 1 2 + 1 6 + 1 12 + 1 20 + ... upto n terms. If the sum of the first six terms of an A.P. with first term -p and common...
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