Find the explicit formula for a geometric sequence 9,19, 39,79,159,...

Ralzereep9h

Ralzereep9h

Answered question

2022-10-25

Find the explicit formula for a geometric sequence 9,19, 39,79,159,...

Answer & Explanation

Liam Everett

Liam Everett

Beginner2022-10-26Added 16 answers

A geometric sequence is a sequence in which there is a common ratio between successive terms. The given sequence is not a geometric sequence, as, for example, 19 9 39 19 .
The sequence is close to a geometric sequence, however. If we add 1 to each term, then the sequence becomes 10,20,40,80,160,... which is a geometric sequence with initial term 10 and common ratio 2.
The general term for a geometric series with common ratio r and initial term a 0 is
a n = a 0 r n , n = 0 , 1 , 2 , ...
In that case, if the general term for the given series is b n , we have
b n + 1 = 10 2 n
Subtracting 1 gives us our result:
b n = 10 2 n - 1 , n = 0 , 1 , 2 , ...

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?