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

I just tried teaching this to myself on the spot, so I might be wrong.
let X be the equation you want to find.

X = a r^(n-1) is the geometric sequence equation
where a is the first term
r is the rate
and n is the output term

@sleepyjess

Answer 2

so with this, we can get the two equations

a r^(2-1) = -36
and
a r^(5-1) = 2304

do you see where I got that? :)

Answer 3

we can simplifyish those two into

a r^1 = -36
and
a r^4 = 2304

just simplifying the exponent part ;)

now this is like the substitution solving method idea
take the first equation, solve for a
we get
a = -36 / r right?
then let's substitute it into the second equation :)

[(-36)/r]*r^4 = 2304
\[\frac{ -36 }{ r }*r^4 = 2304\]
solve for r

Answer 4

once you get r
plug it back into a = -36 / r = ?

then plug all that back into
X = a r^(n-1)
so you would end up with X = (#)*(#)^(n-1) <-- as in keep the n variable in your final answer

Answer 5

source: example 2 http://hotmath.com/hotmath_help/topics/nth-term-of-a-geometric-sequence.html

Answer 6

Sorry, there was an armadillo in our garage....

Answer 7

take a look at what I've written and tell me if you're still confused ^_^

Answer 8

kinda

Answer 9

lol what part? I can try to explain again

Answer 10

@iambatman I feel like I might be doing this wrong? or no?

Answer 11

I don't really get any of it :/

Answer 12

@e.mccormick

Answer 13

read through what I typed again carefully and try to get it
I'm out for the night and will hand you the answer tomorrow morning if you still don't get it