Question

Geometric Sequences...could someone please check my answer?

Answer 1

The question is:
What is the 6th term of the geometric sequence where a_1 = −4,096 and a_4 = 64?

Answer 2

The answer choices are:
-1
1
-4
4

Answer 3

I calculated -4, but I'm not sure if that's correct or not.

Answer 4

@satellite73 and/or @ranga Could you please check this for me?

Answer 5

a2 = a1*r
a3 = a2*r = a1*r^2
a4 = a3*r = a1*r^3
64 = -4096 * r^3
solve for r.

Answer 6

a5=a4*r
a6=a5*r = a4*r^2 = 64*r^2. Plug r found earlier.

Answer 7

I calculated 4 this time...

Answer 8

The numbers are decreasing. |r| must be less than 1.

Answer 9

Ah, I forgot about that rule. Then it would be -1, wouldn't it?

Answer 10

I don't know how I kept coming up with 4, though.

Answer 11

\[
64 = -4096 * r^3\\
r^3 = -\frac{64}{4096} = -\frac{1}{64}\\
r = -\frac{1}{4}
\]

Answer 12

I'm a bit confused, because that isn't one of my choices.

Answer 13

That is "r". You have to use r and a4 to find a5 and then a6 as they are asking for the sixth term.

Answer 14

a5=a4*r = 64 * (-1/4) = -16
a6=a5*r = (-16) * (-1/4) = ?

Answer 15

I calculated 4 again. Is that the correct answer?

Answer 16

Yes.
Oh you were saying you have been getting the final answer as 4 all along? In one of my replies I said solve for "r" and your response was you were getting 4. But r is -1/4. The final answer is 4.

Answer 17

Thank you so much for your time and help! I really appreciate it! :))

Answer 18

You are welcome.