Question

Plz help!

There is a certain infinite geometric series whose first term and common ratio are both real numbers, each of whose terms is the cube of the first series’ terms, is 1. Obtain the common ratio of the first series.

Answer 1

The common ratio of the first G.P. series will be the cube root of the common ratio of the second G.P. series.

Explanation:

Let us assume that the first series has first term a and the common ratio r and is given by

a, ar, ar², ar³, ......... up to infinite terms

It is given that the terms of the second series are a cube of the corresponding terms of the first series.

So, the second series is
`a^(3), a^(3) r^(3) , a^(3) r^(6), a^(3) r^(9), ......` up to infinite terms.

So, it is clear that the second series is a G.P. series with first term a³ and common ratio r³.

Therefore, the common ratio of the first G.P. series will be the cube root of the common ratio of the second G.P. series. (Answer)