Question

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

Answer 1

the summation of 4 times negative 3 to the n minus 1 power, from n equals 4 to 15.

Explanation:

Answer 2

`a_n=5 \ for \ n=1 \\ a_n=-10 \ for \ n=2 \\ a_n=20 \ for \ n=3`

You can see it's a geometric sequence because the ratio is constant (
`(a_3)/(a_2)=(a_2)/(a_1)`).
The nth term of a geometric sequence:

`a_n=a_1 * r^(n-1)`


`a_1=5 \\ r=(a_2)/(a_1)=(-10)/(5)=-2 \\ \\ a_n=5(-2)^(n-1)`

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:

`\sum^(15)_(n=4) 5(-2)^(n-1)`