Question

Identify the 12th term of a geometric sequence where a1 = 8 and a6 = -8,192.
Select one:
A. 134,217,728
B. 33,554,432
C. -33,554,432
D. -134,217,728

Answer 1

Umm ok so here's what I'm thinking...

Answer 2

To get from one term to the next, we multiply by some `common ratio` yes?
Let's call it r.

So to get from a1 to a2,\[\Large\rm a_2=r a_1\]We multiply by r, yah?
To get from a2 to a3, we multiply by r again,\[\Large\rm a_3=r a_2\]\[\Large\rm a_3=r^2a_1\]So we if keep going along like this, we eventually get,\[\Large\rm a_6=r^5a_1\]And we can plug in the information they gave us to try and find our common ratio:\[\Large\rm -8192=8r^5\]Solving for r:\[\Large\rm r=\sqrt[5]{\frac{-8192}{8}}\]And then to get the 12th term of the sequence, we just take our first term and multiply it by the common ratio 11 times.

\[\Large\rm a_{12}=a_1 \left(r\right)^{11}\]

Answer 3

(8)^11

Answer 4

No we're raising the `common ratio (r)` to the 11th power.
You have to solve for r using the information I gave you above.

Then multiply that huge number by 8.

Answer 5

Is the answer C?

Answer 6

Yay good job \c:/

Answer 7

Sweet Thanks!