Question

Given the following series, what is the sum of the first 10 terms?
10+ (-20) + 40'+(-80)+...

Answer 1

The series is an alternating one (has one term positive, one negative) and each term is twice the previous

Let's see what the first 10 terms of the series are:

$\begin{gathered} 10 \\ -20 \\ 40 \\ -80 \\ 160 \\ -320 \\ 640 \\ -1280 \\ 2560 \\ -5120 \end{gathered}$

Now we can add them all:

$10-20+40-80+160-320+640-1280+2560-5120=-3410$

The answer is -3410