Question

MEDAL!

Find the next three terms in each sequence.

1, -3, 9, -27, 81...

Answer 1

Can someone help me derive the recursive formula for this sequence as well to find the next three terms?

Answer 2

What is the pattern that you see?

Answer 3

I know that to get to the next term you need to multiply by -3.

Answer 4

Alright, well now you know how to find the next 3 terms.

Answer 5

But I want to find the recursive formula for this problem to help me easily get to the solution.

Answer 6

As for the recursive formula, it looks something like this:
An = -3^n-1

Answer 7

How did you get that?

Answer 8

-3 is what each value changes by, so when you plug the first term, you get.
An = -3^(1-1)
An = -3^0 = 1
For the second
An = -3^(2-1)
An -3^1 = -3
etc. etc.
It's a geometric sequence.

Answer 9

An = n^(n-1), where n is the amount it changes each time.

Answer 10

*the first N.

Answer 11

So how did you know that you needed to make (n - 1) as an exponent to the nth term?

Answer 12

That's the equation for a geometric recursive formula?

Answer 13

They will always have (n-1)

Answer 14

Sorry I didn't learn about geometric recursive formula yet. But in those formulas, will (n-1) always be raised as a power?

Answer 15

Yes, for geometric ones it will always be that way.

Answer 16

Thank you!