Arts (English Medium) Class 11 - CBSE Question Bank Solutions

If the sum of n terms of an A.P. is (pn + qn²), where p and q are constants, find the common difference.

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18^th terms

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.

Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`

The ratio of the sums of m and n terms of an A.P. is m²: n². Show that the ratio of m^th and n^thterm is (2m – 1): (2n – 1)

if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^th and (m – 1)^th numbers is 5:9. Find the value of m.

A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30^th installment?

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

The p^th, q^th and r^th terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0