A geometric sequence is defined by the explicit formula a_n=5(−3)_(n−1), what is the recursive formula for the nth term of this sequence?

Jadon Camacho

Jadon Camacho

Answered question

2022-11-04

A geometric sequence is defined by the explicit formula a n = 5 ( - 3 ) n - 1 , what is the recursive formula for the nth term of this sequence?

Answer & Explanation

Ryan Davies

Ryan Davies

Beginner2022-11-05Added 18 answers

I assume the formula is: a n = 5 ( - 3 ) n - 1
To calculate the recursive formula first we can calculate some terms of the sequence:
a 1 = 5 ( - 3 ) 1 - 1 = 5 ( - 3 ) 0 = 5
a 2 = 5 ( - 3 ) 2 - 1 = 5 ( - 3 ) 1 = - 15
a 3 = 5 ( - 3 ) 3 - 1 = 5 ( - 3 ) 2 = 45
From these calculations we see that the first term is a 1 = 5 and each other term comes from multiplying previous one by −3.
This algorithm can be written as the recursive formula:
{ a 1 = 5 a n + 1 = - 3 a n

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?