Question

Question: The third and seventh terms of a geometric sequence are 3/4 and 12 respectively.
A. Find the 10th term
B. What term is equal to 3072
Answers:
A. ±96
B. 15th

Please tell me how we arrive at those answers. I'm a bit confused because the common ratio I get is quite weird (it's in fraction) and my calculator can't even solve it. I first got the difference between the 3rd and 12th terms and got 45/4 and then divided that by 4 to get the common difference of 45/16. Tell me what's wrong. thank you :)

Answer 1

Look at this and scroll down to #8.

I have trouble find the first term if it is not given...

let me try....

an = a1 * r^(n-1)
12 = 3/4 * r^(5-1)
12 = 3/4 * r^4
48/3 = r^4
16 = r^4
2 = r

does that look right to you ?

Answer 2

oops....I forgot this...
http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm

Answer 3

So did you regard the 3rd term as 1st and solve it?

Answer 4

it is not solved, I just got the difference as being 2

Answer 5

Yes, but the 2 there is a common ratio right?

Answer 6

yes....thats what I got....I can solve for the 10th term, if you think the common ratio is correct. Like I said, I am not good at finding the first term if it is not given, so I am not sure if the common ratio is correct.I think so, but not 100% sure

Answer 7

So regarding 3rd term as 1st, in order to find out the 100th term, do we do 3/4(2^98-1)
So 3/4(2^97)? Shouldn't that be the answer to A IF the common ratio is correct?

Answer 8

I solved B, I'm a bit confused with A though. I think that's right but I don't know how to simplify that 3/4(2^97)

Answer 9

wait....to find the first term you kinda work backwards....3rd term is 3/4, common ratio is 2.....3/4 * 1/2 = 3/8 <-- 2nd term...3/8 * 1/2 = 3/16 <-- first term..

let me check...
3/16 x 2 = 6/16 = 3/8 (2nd term
3/8 x 2 = 6/8 = 3/4 (3rd term
6/8 x 2 = 12/8 = 6/4 = 3/2 (4th term
3/2 x 2 = 6/2 = 3 (5th term
3 x 2 = 6 (6th term
6 x 2 = 12 (7th term
yes.....2 is common difference and 1st term is 3/16

Answer 10

an = a1 * r^(n - 1)
n = 10
a1 = 3/16
r = 2

a10 = 3/16 ( 2^(10 - 1)
a10 = 3/16 * 2^9
a10 = 3/16 * 512
a10 = 1536/16
a10 = 96

you might better get a second opinion on this

Answer 11

haha alright, thank you so much :)

Answer 12

I tried....I really hope it is correct :)