Find the sum of first 20 terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77.

Find the sum of the first 20 terms of the arithmetic progression having the sum of first ten terms as 52 and the sum of the first 15 terms as 77.

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.

Find the sum of first n terms of the G.P. 256, 64, 16,…

A sequence of integers a_1+a_2++a_n satisfies a_(n+2)=a_(n+1)-a_nforngeq1 . Suppose the sum of first 999 terms is 1003 and the sum of the first 1003 terms is -99. Find the sum of the first 2002 terms.

Two arithmetic progressions have the same numbers. The reatio of the last term of the first progression to the first term of the second progression is equal to the ratio of the last term of the second progression to the first term of first progression is equal to 4. The ratio of the sum of the n terms of the first progression to the sum of the n terms of teh first progression to the sum of the n terms of the second progerssion is equal to 2. The ratio of their first term is

Find the sum of first six terms of the G.P. 5, 15, 45, …

The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12^("th") terms.

An infinite G.P has first 13 term as a and sum 5 , then