Question

Please help me solve this equation

Answer 1

-85

Explanation:

We are given the equation
`E^8_(n=1)`
`(-2)^(n-1)` and are asked to evaluate it.

This can be solved using the geometric sequence, but first we have to determine our "r", "n", and
`a_(1)`.

Of course
`a_(1)` is equal to 1. Therefore,

`a_{1` = 1

`r=`

`n=`

(-2) is the change per number in the sequence, therefore -2 is our "r".

`a_{1` = 1

`r=-2`

`n=`

The number "8" on
`E^8_(n-1)` represents the "n". Therefore 8 is our "n".

`a_(1)=1`

`r=-2`

`n=8`

Use the geometric sequence sum formula and substitute :

`a_(1) (1-r^n)/(1-r)`

`1* (1-(-2)^8)/(1-(-2))`

`1* (1-(-2)^8)/(1+2)`

`1* (1-256)/(1+2)`

`1* (-255)/(3)`

`1 * -85`

`-85`