If the sum of first 10 terms is 33 times the sum of first 5 terms of G.P., find the common ratio.

If the sum of first 10 terms of an A.P. is 4 times the sum of its first 5 terms, then find the ratio of first term and common difference.

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.

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P., and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

The first term of a G.P. is 2 and the sum to infinity is 6. Find the common ratio.

Find the sum of first n terms and the sum of first 5 terms of the geometric series : 1+2/3+4/9 + .........

If the sum of the first two terms and the sum of the first four terms of a geometric progression with positive common ratio are 8 and 80 respectively then what is the 6th term ?