Question

If r = 3 and the sum of 6 terms of the geometric series is 3640, what is the first term?

Answer 1

First term is `10`

Explanation:

In a geometric series, if `a` is the first term and ratio between a term and its preceding term is `r`, then sum of first `n` terms ia given by

`a(r^n-1)/(r-1)`

As `r=3` and sum of first `6` terms is `3640`, we have

`a(3^6-1)/(3-1)=3640`

hence `a(729-1)/(3-1)=(axx728)/2=3640`

or `364a=3640` and hence

`a=10`.