If the first term of an infinite geometric series is equal to twice of the sum of all the terms that follows it, then the value of r is?

Question

1/3, 1, 1/2 or 2? how?

Answer 1

Assuming that the common ratio, r, satisfies -1<r<1, the sum of the series is a/(1-r), where a is the first term of the series.

 

If a = 2[a/(1-r) - a], then a = 2a/(1-r) - 2a

 

                                     3a = 2a/(1-r)

 

                                     3a - 3ar = 2a

 

                                         - 3ar = -a

 

                                              r = 1/3