Question

15. Determine if the following sequence is arithmetic or geometric. What is the common difference/ratio? -2,4,-8, 16, ... a. arithmetic, 2 b. arithmetic, - 2 c. geometric, 2 d. geometric, - 2

Answer 1

Answer:

d. geometric, - 2​

Explanation:

An arithmetic sequence is a sequence in which the next term is obtained by adding/subtraction of a constant to the previous term.

A geometric sequence is a sequence in which the next term is obtained by multiplying/dividing the previous term by a number.

Given the sequence

$\begin{gathered} -2,4,-8,16,\ldots \\ \frac{4}{-2}=-2 \\ -\frac{8}{4}=-2 \\ \frac{16}{-8}=-2 \end{gathered}$

The sequence is geometric and the common ratio is -2.