Question

How do you find `S_n` for the geometric series `a_1=80`, r=-1/2, n=7?

Answer 1

`53.75`

Explanation:

Just use the formula for finding the sum of `n` terms while the common ratio.

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

Substituting the values,

`S_n = (80(1 - (-1/2)^7))/(1 - (-1/2)) = (80 * (1 + 1/128))/(1 + 1/2) = (80 * 129/128)/(3/2) = (80.625)/(1.5) = 53.75`

It makes sense that The sum is actually less than the first term of the Geometric Progression, As `r = -1/2 < 1`