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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

User Csinchok
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1 Answer

5 votes

Answer:


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 }

User Bilal Rammal
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