Question

The sequence an can be defined by the formula an=3(23)n. Which of the following is a recursive definition of the formula?

A. a1=2 an+1=2an3
B. a1=3 an+1=2an3
C. a1=2 an+1=an+23
D. a1=3 an+1=an+23

Answer 1

`a_ {1}=2 \\ a_ {n + 1}= (2)/(3) a_ {n }`

Explanation:

The sequence is defined explicitly as

`a_n=3( (2)/(3) )^n`

The first term of this sequence is

`a_1=3( (2)/(3) )^1 = 2`

The recursive formula is given as:

`a_n=ra_ {n - 1}`

Or

`a_ {n + 1}=ra_ {n }`

where

`r = (2)/(3)`

is the common ratio.

The recursive formula is therefore:

`a_ {1}=2 \\ a_ {n + 1}= (2)/(3) a_ {n }`