Question

How do you find the sum of the first 16 terms of `-90+30+(-10)+10/3+...`?

Answer 1

Approximately `67.5`

Explanation:

The general equation for the sum of the first `n` terms of a geometric series with initial value `a_1` and a common ratio of `r` is:
`color(white)("XXX")sum_(i=1)^n a_i=a_1((1-r^n)/(1-r))`

In this case, the sum of the first `15` terms with an initial value of `90` and a common ratio of `(-1/3)` is
`color(white)("XXX")90 * ((1-(-1/3)^15)/(1-(-1/3)))`

`color(white)("XXX")~~67.5000047` (assuming I used my calculator correctly)