Find the 8th term of the geometric sequence 5, -15, 45, ...5,−15,45,...

The 8th term of the geometric sequence 5, -15, 45, ... is:

Step-by-step explanation:

Given the geometric sequence

5, -15, 45, ...

The first element of the geometric sequence is

A geometric sequence has a constant ratio 'r' and is defined by  

computing the ratios of all the adjacent terms

The ratio between all the adjacent terms is the same and equal to

substituting , and in the nth term

Determining the 8th term:

We have already got the nth term

substituting n = 8 to determine the 8th term

Therefore, the 8th term of the geometric sequence 5, -15, 45, ... is:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction