Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.

Answer 1

Need some helppp :(

Answer 2

We know that the second term is: (a)(r) and the 5th term is: (a)(r^4)

Also, 2304/(-36) is the 5th term divided by the 2nd term which is -64
That is also: [(a)(r^4)] / [(a)(r)] = r^3

So, r^3 = -64 and r = -4

So, the 2nd term, -36, is (a)(r) = (a)(-4), so "a" = 9

We now have "a" and "r" and the general expression for the nth term is:

(9)(-4)^(n-1)

And remember that exponentiation takes precedence over multiplication, so only the
"-4" is being raised to the "n-1" power.

Answer 3

All good now, @worne001 ?

Answer 4

That problem is much more difficult than it appears, lol.. i guess I kind of understand..This is another exampled problem I have, kind of the same format..
Find an explicit rule for the nth term of the sequence. (is this the same process?)


-5, -25, -125, -625, ...

Answer 5

Okay, thank you so much ! :D

Answer 6

uw! Good luck to you in all of your studies and thx for the recognition! @worne001 See you in the new post.