Question

How many terms of the series 2 + 6 + 18 + ............ must be taken to make the sum equal to 728 ?

Answer 1

The series 2,6,18…. is a Geometric Progression i.e the adjacent terms in the series defer by a factor of ‘r’.

In this case the first term ‘a’ is 2 and the common ratio ‘r’ is 6/2 which is 3.

Let us assume you have to sum ’n’ terms in this series to get the sum 728.

Sum of n terms in a Geometric Progression is $\frac{a\times (r^n-1)}{(r-1)}$

=> $\frac{2(3^n-1)}{(3–1)}$ = 728 => $3^n-1$ = 728 => $3^n$ = 729 => n = 6