The common ratio of a G.P. is `-4/5` and the sum to infinity is `80/9`. Find the first term.

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

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 three consecutive terms of an A.P. is 9 and the sum of their squares is 35. Find the terms.

The sum of first three terms of a G.P. is 7 and the sum of their squares is 21. Determine the first five terms of the G.P.

The third term of an A.P. is 25 and the tenth term is -3. Find the first term and the common difference.

The third term of an A.P. is 25 and the tenth term is - 3. Find the first term and the common difference.

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.

The sum of the third and the seventh term of an A.P. is 6 and their product is 8. Find the sum of first sixteen terms of an A.P.

The sum of an infinite number of terms of a G.P. is 15 and the sum of their squares is 45. Find the G.P.