Question

Having an issue with these...Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...

Answer 1

This one will actually be easier than the last one since we are given the first term. That way, we already know "a" which is -5. We also can re-write the sequence:

-5(1, 5, 25, 125, . . . )

And since the general expression for the nth term is (a)[r^(n-1)]

we can see we are dealing with powers of "5":

(-5)[5^(n-1)]

Answer 2

All good now, @worne001 ?

Answer 3

okay, cool. if the numbers were positive, the same formula and steps are used right?

Answer 4

Yes. Another comment about this problem, though. It looks at first like you can also write:

(-1)[5^n]

And that would be ok, but it is better to show "r" with a "n-1" power.

Answer 5

So, you just go with the first term having a factor in it of r^(n-1) which is just "1".

Answer 6

Okay, thanks @tcarroll010

Answer 7

You are very welcome! @worne001