Question

Problem ID: PRABK2AZ

1. Use the first five terms of sequence
to define the sequence recursively using function notation.
2.5, 7.5, 22.5, 67.5, 202.5,...

Answer 1

Answer: f(n+1) = 3 f(n)

Explanation:

• A recursive formula is used to determine each term of a sequence using preceding term or terms.

Given sequence : 2.5, 7.5, 22.5, 67.5, 202.5,...

Here,

`2.5* 3=7.5\\7.5*3= 22.5\\22.5* 3= 67.5\\67.5*3=202.5`

Common ratio = 3

Let f(n) be a term in this sequence then the next term will be f(n+1) = 3 f(n), where n is a natural number .

Required recursive formula : f(n+1) = 3 f(n)