Question

What is the equivalent recursive definition for an = 12+ (n - 1)3?

A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3

Answer 1

`A_1 = 12`

`A_n = A_(n-1) + 3`

Explanation:

Given

`A_n =12+(n-1)3`

Required

Write as recursive

We have:

`A_n =12+(n-1)3`

Open bracket

`A_n =12+3n-3`

`A_n =12-3+3n`

`A_n =9+3n`

Calculate few terms

`A_1 =9+3*1 = 9 + 3 = 12`

`A_2 =9+3*2 = 9 + 6 = 15`

`A_3 =9+3*3 = 9 + 9 = 18`

The above shows that the rule is to add 3.

So, we have:

`A_1 = 12`

`A_n = A_(n-1) + 3`