Question

Find the explicit formula for the sequence? -1,4,16,64

Answer 1

`f(n)=4^(n-1)`

Step-by-step explanation:

Given the sequence

`1,4,16,64`

We observe that the next term of the sequence is obtained by multiplying the previous term by 4.

This is an example of a geometric sequence.

The nth term of a geometric sequence is:

`\begin{gathered} U_n=ar^(n-1) \\ \text{First term, a=1} \\ \text{Common ratio, r =4} \end{gathered}`

Therefore, the nth term is:

`U_n=1*4^(n-1)`

The explicit formula for the sequence is:

`f(n)=4^(n-1)`