Question

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

Find the common ratio of the given sequence, and write an exponential function which represents the sequence. Use n = 1, 2, 3, ...
A) 3; f(n) = 2(3)n-1
B)
1
3
; f(x) = 2(3)n-1
C) 3; f(n) = 2(
1
3
)n-1
D)
1
3
; f(n) = 2(
1
3
)n-1

Answer 1

A

Explanation:

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Answer 2

3;
`f(n)=2(3)^(n-1)`

Explanation:

The given sequence is

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

The first term is
`f(1)=2`

The common ratio is obtained expressing a subsequent term over a previous term.

The common ratio is
`r=(6)/(2) =3`

The the nth term of the sequence is given by:

`f(n)=f(1)(r^(n-1))`

`f(n)=2(3)^(n-1)`

The exponential function which represents the sequence is

`f(n)=2(3)^(n-1)`