Question #b6ffe

2 Answers
Jul 28, 2017

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.

Jul 28, 2017

-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