English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Let S_n denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = S_n − kS_n−1 + S_n−2, then k =

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is

If S₁ is the sum of an arithmetic progression of 'n' odd number of terms and S₂ the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]

If in an A.P. S_n = n²p and S_m = m²p, where S_r denotes the sum of r terms of the A.P., then S_p is equal to 

If S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n, then S_3n : S_n is equal to

In an AP. S_p = q, S_q = p and S_r denotes the sum of first r terms. Then, S_p+q is equal to

If S_r denotes the sum of the first r terms of an A.P. Then , S_3n: (S_2n − S_n) is

If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is 

The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is

Sum of n terms of the series  `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.

The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\]  are in A.P. Then, x =

The nth term of an A.P., the sum of whose n terms is S_n, is

The common difference of an A.P., the sum of whose n terms is S_n, is

If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their n^th terms are in the ratio

If S_n denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\]  is independent of x, then

If the first term of an A.P. is a and nth term is b, then its common difference is

The sum of first n odd natural numbers is ______.