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=(4)/(-2)=-2`

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

`r=(-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*(-1023)/(3)=682 \end{gathered}`

The sum is 682