Question

5. 2,4,8, 16,...
Recursive:
Explicit

Answer 1

Recursive:
`x_n=2(x_(n-1))`

Explicit:
`x_n=2(2)^(n-1)`

Explanation:

First, note that this is a geometric sequence. This is because each term is 2 times its previous term.

The standard recursive form for a geometric sequence is:

`x_n=r(x_(n-1))`

Where n is the nth term, so n-1 is the previous term, and r is the common ratio.

Substitute 2 for r.

Therefore, our recursive formula is:

`x_n=2(x_(n-1))`

The standard form of the explicit formula for geometric sequences is:

`x_n=ar^(n-1)`

Again, r is the common ratio and a is the initial term.

The common ratio is 2 and the initial term is 2. So, substitute:

`x_n=2(2)^(n-1)`

And that's our explicit formula.

And we're done!