Question

How do you find the sum of the first 18 terms of `7+(-21)+63+(-189)+...`?

Answer 1

Sum of first `18` terms is `-1743392196`

Explanation:

As here `-21/7=63/(-21)=(-189)/63=-3`, here we have a geometric series with first term as `7` and common ratio as `-3`.

As in a geometric series with first term as `a` and common ration `r`,

sum of first `n` terms is given by `(a(1-r^n))/(1-r)`

Hence, in the given series sum of first `18` terms is given by

`(18xx(1-(-3)^18))/(1-(-3))`

= `(18xx(1-387420489))/4`

= `-(18xx387420488)/4`

= `-18xx96855122`

= `-1743392196`