Question

Question #b6ffe

Answer 1

Two ways

Explanation:

We observe that these are the first few terms of a geometric sequence because the ratio of each term to the term before it is the same value ... -3.

For this sum,
the first term is `a_0 = 1`.
The common ratio is `r = -3`.
Since `-243 = (-3)^5`, there are six terms altogether.

By the formula for summation
`S_5 = (1-r^6)/(1 - r)`
`S_5 = (1-(-3)^6)/(1 - (-3))`
`S_5 = (1-729)/(1 +3)`
`S_5 = -728/4`
`S_5 = -182`

For this particular sum, we have

`1 - 3 + 9 - 27 + 81 - 243`.

Add these up to get `-182`.

Answer 2

`-182`

Explanation:

`"the sum to n terms of a geometric series is"`

`•color(white)(x)S_n=(a(1-r^n))/(1-r)`

`"where a is the first term, r the common ratio and n the"`
`"number of terms"`

`"here " a=1, r=(-3)/1=9/(-3)=-3 ,n=6`

`rArrS_6=(1(1-(-3)^6))/(1-(-3)`

`color(white)(rArrS_6)=(1-729)/4=-182`