SOLUTION: In the geometric sequence find r and the 10th term. a) 4, 12, 36,108... b) 972, -324, 108, -36... Not really sure what to do here. Thank you.

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Question 598796: In the geometric sequence find r and the 10th term.
a) 4, 12, 36,108...
b) 972, -324, 108, -36...
Not really sure what to do here. Thank you.
Found 2 solutions by KMST, Earlsdon:
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
A geometric sequence is a sequence of numbers (called terms) where each number is the product of the one before times a fixed number, called the common ratio. So, with
=the nth term
=the term after and
=the common ratio
we have the relations
<-->
and if we call the first term then

In 4, 12, 36,108... , , and we see that , the same as and
so applying we find that

In 972, -324, 108, -36... , , and we see that ,
so applying we find that

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
In geometric sequences, r (known as the common ratio) is the ratio of one of the terms and the preceding term.
For the first sequence, r can be found by dividing the second term by the first term, or the third term by the second term:
a) or
The nth term is found by:
where: is the first term, r is the common ratio, and n = the number of the term.
So for the 10th term, n = 10 and:

b) The common ratio, r, is:

and the 10th term is:
and , so...

Approx.