SOLUTION: Write a rule and find the given term in the geometric sequence described below. Show your work. What is the eighth term when the first term is -4 and the common ratio is -1/2?

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Question 255741: Write a rule and find the given term in the geometric sequence described below. Show your work. What is the eighth term when the first term is -4 and the common ratio is -1/2?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for geometric sequences is
(i) Tn+=+a%2Ar%5E%28n-1%29
using given infpormation, we get
(ii) -4+=+a%2A%28-1%2F2%29%5E%281-1%29
this is
(iii) -4+=+a%2A%28-1%2F2%29%5E%280%29
or
(iv) a+=+-4
Now, (i) becomes
(v) T%28n%29+=+-4%28-1%2F2%29%5E%28n-1%29
the 8th term is
(vi) T%288%29+=+-4%28-1%2F2%29%5E%288-1%29
or
(vii) T%288%29+=+-4%28-1%2F2%29%5E%287%29
T%288%29+=+4%2F128
T(8) = 1/32