The 5th term of a geometric sequence is 45 and the 8th term is 360. How do you determine the 20th term?

Kameron Wang

Kameron Wang

Answered question

2022-11-18

The 5th term of a geometric sequence is 45 and the 8th term is 360. How do you determine the 20th term?

Answer & Explanation

trivialaxxf

trivialaxxf

Beginner2022-11-19Added 21 answers

First we need to find the ratio, r and the first term:a.
We know that a r 5 = 45 and a r 8 = 360 .
To determine r can divide the 8th term by the 5th term like so:
a r 8 a r 5 = 360 45
The as will cancel and the rest will simplify to:
r 3 = 8
r = 2
To find a simply substitute r into either of the known terms, i.e:
a 2 5 = 45 a = 45 2 5 = 45 32
Now we can find the twentieth term:
a r 20 = 45 32 2 20 = 1474560

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?