Question

For the sequence -3, -12, -48, … how do you find the sum of the first 12 terms?

Answer 1

Use the formula `sum_0^n = (a(1-r^n))/(1-r)` where `a` is the first term, `r` is the common ratio and `n` is the number of terms.

Explanation:

The sequence here is `-3, (-3*4), (-3*4*4),......`

So the `n`th term is `(-3)*4^(n-1)`

The first term is `-3` and the common ratio is `4`.

`sum_1^12 = ((-3)(1-4^12))/(1-4) =((-3)(-16777215))/(-3)`

`=-16777215`