Question

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

n an
1 4
2 −12
3 36

Answer 1

The answer is in the picture bellow

Explanation:

I took the quiz

Answer 2

It's a geometric sequence.


`4,-12,36,... \\ \\ a_1=4 \\ r=(a_2)/(a_1)=(-12)/(4)=-3 \\ \\ a_n=a_1 * r^(n-1) \\ a_n=4 * (-3)^(n-1) \\ a_n=4 * (-3)^(-1) * (-3)^n \\ a_n=4 * (-(1)/(3)) * (-3)^n \\ a_n=-(4)/(3)(-3)^n`

It's the sum for term 4 through term 15.


`\boxed{ \sum\limits_(n=4)^(15) ((4)/(3)(-3)^n)}`