Sequence and Series questions
1035 published questions with worked solutions.
- The sum of first four terms of a geometric progression (G.P.) is 65 12 and the sum of their respective reciprocals is 65 18 . If...
- If N is the number of ways in which 3 distinct numbers can be selected from the set 3^1,3^2,3^3, ,3^ 10 so that they form a G.P....
- Let n=27. Let the number of ways of selecting three numbers from 1,2,3, ,n in A.P. be p^2 then find p.
- _ k=1 ^ k (1+ 1n )^ k-1 =
- The value of 1 2 3 4+2 3 4 5+3 4 5 6+ +n(n+1)(n+2)(n+3), is
- The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is
- The remainder on dividing 1+3+3^2+3^3+ +3^ 2021 by 50 is
- If a,b,c be in arithmetic progression, then the value of (a+2b-c)(2b+c-a)(a+2b+c) is
- If the sum to 2n terms of the AP 2,5,8,11, is equal to the sum to n terms of the AP 57,59,61,63, , then n is equal to
- If 1, _3 3^ 1-x +2 , _3 (4 3^x-1 ) are in AP, then x equals
- If twice the 11^ th term of an AP is equal to 7 times its 21^ st term, then its 25^ th term is equal to
- The sum of the integers from 1 to 100 which are divisible by 3 and 5, is
- Let T_r be r^ th term of an AP whose first term is a and common difference is d. If for some positive integers m,n, m n, T_m= 1n...
- If a_1,a_2,a_3,a_4,a_5 and a_6 are six arithmetic means between 3 and 31, then a_6-a_5 and a_1+a_6 respectively equals
- If a_1,a_2,a_3, ,a_n are the n arithmetic means between a and b, then 2 _ i=1 ^na_i equals
- If a^2,b^2,c^2 are in AP, then which of the following is also an AP?
- If 5+9+13+ +n terms 7+9+11+ +12 terms = 5 12 , then n is equal to
- If the arithmetic mean of a and b is a^n+b^n a^ n-1 +b^ n-1 , then the value of n is
- If S_n=nP+ 12n(n-1)Q, where S_n denotes the sum of the first n terms of an AP, then the common difference is
- The sum of all two digit natural numbers which leave a remainder 5 when divided by 7 is equal to
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