Question

How do you find `S_n` for the geometric series `a_1=1296`, `a_n=1`, r=-1/6?

Answer 1

1111

Explanation:

One important observation to make here is, that first term is 1296 that is `6^4` and nth term is `6^0` =1. That means the series consists of 5 terms. So n=5. Now

Sum of a geometric series is given by the formula `a (1-r^n)/(1-r)`

Here a = 1296, `r= (-1/6)`, thus Sum= `1296 (1- (-1/6)^n)/ (1+1/6)` = `1296 (1+1/7776)/(7/6)` = 1111.

The sum can be found more easily by writing the 5 terms of the series 1296, -216, 36,-6 ,1 and adding.