Question

What is the sum of a 6–term geometric series if the first term is 22 and the last term is 1,299,078?

Answer 1

Sum of the series is `1,461,460`

Explanation:

In a geometric series `{a,ar,ar^2,ar^3,.........}` whose first term is `a` and ratio between a term and its preceeding tetm is `r`, the `n^(th)` term is given by `ar^(n-1)` and sum of first `n` terms is given by `axx(r^n-1)/(r-1)`.

Here as first term is `22` and sixth term is `1299078`, as such `a=22` and `ar^5=1299078` or `r^5=1299078/22=9^5` i.e. `r=9`.

Hence sum of the series is `22xx(9^6-1)/(9-1)=22xx66,430=1,461,460`