SOLUTION: in the geometric sequence 6,12,24,48, which term is 768?

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Question 1086787: in the geometric sequence 6,12,24,48, which term is 768?
Found 2 solutions by htmentor, jim_thompson5910:
Answer by htmentor(1343) About Me  (Show Source):
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The n-th term of a geometric sequence is a_n = a*r^(n-1) where r is the common ratio and a is the 1st term.
In this case, r = 2, and the 1st term is 6.
Thus a_n = 768 = 6*2^(n-1)
768/6 = 128 = 2^(n-1)
Since 2^7 = 128 -> n - 1 = 7, or n = 8
786 is the 8th term.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First term = a = 6

common ratio = r = (second term)/(first term) = 12/6 = 2

In summary so far: a = 6, r = 2

The nth term a%5Bn%5D of the geometric sequence is

a%5Bn%5D+=+a%2Ar%5E%28n-1%29

a%5Bn%5D+=+6%2A2%5E%28n-1%29

We don't know what n is, but we know that 768 is one of the terms of this sequence (given). So replace all of a%5Bn%5D with 768 and solve for n

a%5Bn%5D+=+6%2A2%5E%28n-1%29

768+=+6%2A2%5E%28n-1%29

768%2F6+=+%286%2A2%5E%28n-1%29%29%2F6 Divide both sides by 6

128+=+2%5E%28n-1%29

2%5E7+=+2%5E%28n-1%29 Rewrite 128 as 2^7

7+=+n-1 The bases are both 2, so the exponents must be equal

7%2B1+=+n-1%2B1 Add 1 to both sides

8+=+n

n+=+8

Answer: The term 768 is the 8th term of the geometric sequence.