Question

−2 + 4 − 8 ... find 10 term

Answer 1

Given the series:

-2 + 4 - 8

Find the sum of the 10 first terms.

First, we need to find the common ratio of the terms:

$r=\frac{4}{-2}=-2$

It can be also calculated with the last two given terms:

$r=\frac{-8}{4}=-2$

So, we have a geometric series with first term a1 = -2 and common ratio r = -2.

The formula to calculate the sum of n terms is:

$S_n=a_1\frac{\text{ }1-r^n}{1-r}$

Applying the formula with n = 10:

$S_{10}=-2\frac{\text{ }1-(-2)^{10}}{1-(-2)}$

Operating:

$\begin{gathered} S_{10}=-2\frac{\text{ }1-1024}{1+2} \\ \\ S_{10}=-2\times\frac{-1023}{3}=682 \end{gathered}$

The sum is 682