Question

What is the common ratio in the following geometric sequence?

3, 12, 48, 192,

With the formula
an = a1 · rn - 1.

Answer 1

The previous problem involved adding a number to get the next term. This one involves multiplying a number to get the next term. Do you see a number that is added to each term to get the next one?

Answer 2

Sorry, multiplied by each term to get the next one.

Answer 3

So you would take an=3 X ?-1

Answer 4

Yes, you're on the right track.

Answer 5

I think the equation is actually an = a1 x r(n-1), however.

Answer 6

Otherwise it wouldn't match the geometric sequence.

Answer 7

So An=3 x the common ratio (n-1)

Answer 8

Exactly.

Answer 9

im confused about the common ratio part... blonde moment lol

Answer 10

Well, just divide each term by the one before it. That will give you the common ratio, which is just a fancy term for what you need to multiply a term in the geometric sequence to get the next term.

Answer 11

Ahh ok

Answer 12

So An=3 x 4 (n-1)

Answer 13

Correct, 4 is the common ratio.

Answer 14

So now we find N?

Answer 15

Well, we weren't given n, and we can't really calculate it. Thankfully, we don't need to. The question only asked for the common ratio of the geometric sequence, which you found.

Answer 16

So now its just 3x4?

Answer 17

Well, the common ratio is just r. a1 is the first term, which is 3, so what you have there is a1 x r.

Answer 18

I know it's totally confusing, but the answer is simpler than the previous problem would suggest.

Answer 19

Yeah it is haha

Answer 20

4?

Answer 21

Yes, that's correct.