What is the product of first `2n+1` terms of a geometric progression ?

If the product of the 4^(th), 5^(th) and 6^(th) terms of a geometric progression is 4096 and if the product of the 5^(th), 6^(th) and 7^(th) - terms of it is 32768, find the sum of first 8 terms of the geometric progression. For any two positive numbers, the three means AM, GM and HM are in geometric progression.

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?

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 ?

If 2nd, 8th, 44th term of an non-cosntant arithmetic progression is same as 1st, 2nd & 3rd term of Geometric progression respectively and first term of arithmetic progression is , then sum of first 20 terms of that arithmetic progression is

The sum of first three terms of a geometric progression is 13/12 and their product is -1 Find geometric progression.

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is

In a geometric progression,if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is

The first two terms of a geometric progression add upto 12. The sum of the third and the fourth term is 48.If the terms of the geometric progression are alternatively positive and negative, then the first term is :