If the first term of a G.P. is 5 and the sum of first three terms is `(31)/5`, find the common ratio

5th term of a G.P. is 2, then the product of first 9 terms is:

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

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 first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the 20th term.

If the first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the sum of first 30 terms.

If the 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

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

The nth term of a G.P. is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is:

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

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.