Question

Find the common ratio of the geometric sequence 18,-72,288,...

Answer 1

Answer:

The common ratio of the geometric sequence is -4

Step-by-step explanation:

Geometric Sequence

A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:

$a_n=a_{n-1}*r$

Where r is the common ratio.

We are given three terms of a geometric sequence:

18,-72,288,...

To find the common ratio, just divide each term by the previous term:

$\displaystyle r=\frac{-72}{18}=-4$

Make sure it's a fixed number and test with the third term:

$\displaystyle r=\frac{288}{-72}=-4$

Since both numbers coincide, the common ratio of the geometric sequence is -4