Question

2, 6, 18, 54. 162,...

The first five terms of a geometric sequence are given above.

Write a recursive function rule for the sequence.

a
f\left(n\right)=3f\left(n\right)+2

b
f\left(n\right)=2n

c
f\left(n\right)=3f\left(n-1\right),\ n1=2

d
f\left(n\right)=3n+2

Answer 1

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Answer:

`\text{c. }f(n)=3f(n-1);f(1)=2`

Explanation:

The first term is 2, so part of the recursive definition is ...

f(1) = 2

The common ratio is 6/2 = 3, so each term is 3 times the previous one. That part of the recursive definition is ...

f(n) = 3·f(n -1)

These two parts of the definition match choice C.