The sum of the first few terms in a geometric progression is 11, the sum of their squares is 341, and sum of their cubes is 3641. Find the terms of the sequence.
In mathematics a geometric progression also known as a geometric sequence. It is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, 162.......
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A geometric sequence is one in which the same number is multiplied or divided by each element to get the next element in the sequence. 2, 4, 8, 16, ... is a geometric sequence.
The terms of the series are: 1, -2, 4, -8, 16 or 16, -8, 4, -2, 1.
You have to set up three equations for the given three conditions and have to solve them. The procedure is time consuming and lengthy so instead of typing that all here I would like you to visit the URL given below in the reference, it explains the entire solution. Hope it clears.