Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.

The p^th term of an A.P. is a and q^th term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.

If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n

Find the sum of first 24 terms of the A.P. a₁, a₂, a₃, ... if it is known that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225.

The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers

Show that (x² + xy + y²), (z² + xz + x²) and (y² + yz + z²) are consecutive terms of an A.P., if x, y and z are in A.P.

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`

If a₁, a₂, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a₂ + cosec a₂ cosec a₃ + ...+ cosec a_n–1 cosec a_n) is equal to cot a₁ – cot a_n 

If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad

In an A.P. the p^th term is q and the (p + q)^th term is 0. Then the q^th term is ______.

The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`

A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?

Find the r^th term of an A.P. sum of whose first n terms is 2n + 3n² 

If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).

If the sum of n terms of an A.P. is given by S_n = 3n + 2n², then the common difference of the A.P. is ______.

If 9 times the 9^th term of an A.P. is equal to 13 times the 13^th term, then the 22^nd term of the A.P. is ______.

If in an A.P., S_n = qn² and S_m = qm², where S_r denotes the sum of r terms of the A.P., then Sq equals ______.

Let 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 ______.