Questions

The sum of the first 6 terms of a GS is 9 times the sum of the first 3 terms. Find the common ratio.

Three numbers are in an arithmetic series and their sum is 18. If the first two numbers are increased by 4 each and the third is increased by 36, they form a geometric series. Find the numbers.

Three numbers are in a geometric series and their product is 1000. If 6 and 7 are added to the second and third terms respectively, they form an arithmetic series, find the numbers.

Three numbers are in a geometrical series and their sum is 15. If 1, 3, and 9 are added to them respectively, they form a geometric series, find the numbers.

The product of three numbers in a GS is 27 and the sum of their products in pairs is 39. Find the numbers.

The sum of three numbers in a geometric series is 31 and their product is 125. Find the numbers.

The sum of the first two terms and four terms of a GP are 3 and 15 respectively. Find the sum of its first six terms, if the common ratio is positive.

The sum of 1$^{st}$ 6 terms of a GP is 28 and sum of first 3 terms is 1. Find its common ratio and first term.

The common ratio of a geometric series is 3 and the sum of its first 4 terms is 80. Find the first term.

The sum of the first 3 terms of a GS is 292 and its common ratio is 8. Find the first term of the series.