Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -24 and 1536, respectively. I know this is basic but can someone explain?

Answer 1

I know have to use the formula for nth term but I just don't know how to apply it.

Answer 2

Wait what?

Answer 3

sequence is \[a,ar, ar^2, ar^3, ar^4, ...\] that is what a geometric sequence looks like

Answer 4

you are told \(ar=-24,ar^4=1536\)

Answer 5

Right!

Answer 6

to find \(r\) divide

Answer 7

Divide 1539 over -24?

Answer 8

\[\frac{ar^4}{ar}=\frac{1536}{-24}\]

Answer 9

So that equals -64.

Answer 10

so
\[\frac{ar^4}{ar}=r^3=-64\]

Answer 11

solve and get \(r=\sqrt[3]{-64}=-4\)

Answer 12

So the second term is -24 and the third is -64.

Answer 13

no you are just finding \(r\)

Answer 14

I am so lost.. :(

Answer 15

But I have never seen a cubed root used to find r..

Answer 16

from algebra, what is
\[\frac{ar^4}{ar}\]?

Answer 17

\[ar^3\]?

Answer 18

no

Answer 19

the \(a\)'s cancel as well

Answer 20

\[r^3\]

Answer 21

OH. I got it.

Answer 22

whew !

Answer 23

So if \[r^3\] is equal to -64

Answer 24

I'm sorry reading math on here is difficult.

Answer 25

yeah you got it

Answer 26

I'm in an upper level math and reviewing this is so weird for me.

Answer 27

\[r=-4\]

Answer 28

right because the cube root is -4.

Answer 29

So if r = -4, the first term is 6?

Answer 30

ok now we got \(r\) what is \(a\)?

Answer 31

I said 6...

Answer 32

ok

Answer 33

So it's \[6 * 4^(n+1)\]

Answer 34

With the n + 1 raised?

Answer 35

?

Answer 36

\[a=6, r=-4\]

Answer 37

terms are
\[6, 6\times (-4), 6\times (-4)^2,6\times (-4)^3,...\]

Answer 38

Am I right?

Answer 39

I'm only looking for the equation..

Answer 40

I don't need the actual terms.