Question

What is the sum of the first thirteen terms in a geometric series with a1=−3 and r=4?

Answer 1

The sum of the first 13 terms of the sequence is -67,108,863.

Explanation:

Sum of the first n terms of a geometric sequence:

The sum of the first n terms of a geometric sequence, with first term
`a_1` and ratio r, is given by:

`S_n = (a_1(1-r^n))/(1-r)`

In this question:

`a_1 = -3, r = 4`

Sum of the first 13 terms:

`S_(13) = (-3(1 - 4^13))/(1-4) = -67108863`

The sum of the first 13 terms of the sequence is -67,108,863.