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:
[tex]a_n=a_{n-1}*r[/tex]
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:
[tex]\displaystyle r=\frac{-72}{18}=-4[/tex]
Make sure it's a fixed number and test with the third term:
[tex]\displaystyle r=\frac{288}{-72}=-4[/tex]
Since both numbers coincide, the common ratio of the geometric sequence is -4
