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

Answer:

$A_1 = 12$

$A_n = A_{n-1} + 3$

Step-by-step 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:

$A_1 = 12$

$A_n = A_{n-1} + 3$