Question

Question 13 (Essay Worth 8 points)

Write the sum using summation notation, assuming the suggested pattern continues.

3, -12, 48, -192, + …

Is this sequence arithmetic or geometric? Explain your answer.

Answer 1

9514 1404 393

Answer:

geometric sequence

Explanation:

The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...

an = 3(-4)^(n-1)

so the sum can be written as ...

`\displaystyle\sum_(n=0)^\infty3(-4)^n`

(Note the summation starts at n=0, corresponding to a first term of 3.)