Question

Write each sequence as a function.

c. an+1 = 3an, a1 = 1, where nn is a positive integer greater than or equal to 1.

Answer 1

`f(x)=3^x` where
`0\leq x`

Explanation:

We are given that a sequence

`a_(n+1)=3a_n,a_1=1`

Where
`n\geq 1`

We have to write a sequence as function.

When n=1

`a_2=3a_1`

`a_2=3(1)=3`

n=2

`a_3=3a_2=3(3)=9=3^2`

`a_4=3a_3=3(9)=27=3^3`

`a_5=3(27)=81=3^4`

Therefore, the given sequence can be write as function

`f(x)=3^x` where
`0\leq x`

Answer 2

Answer:
`f(n)=3^(n-1)`

Explanation:

Given Recursive formula :
`a_(n+1) = 3a_n,`,
`a_1=1`

Then,
`a_2=a_(1+1) = 3a_1=3(1)=3`

`a_3=a_(2+1) = 3a_2=3(3)=9`

`a_4=a_(3+1) = 3a_3=3(9)=27`

We can write it as :
`f(n)=3^(n-1)`

such that

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

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

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

3
`f(3)=3^(3-1)=3^2=9`

Hence, the required function:
`f(n)=3^(n-1)`