SOLUTION: The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term

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Question 753894: The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the n-th term of a geometric sequence is
a%28n%29+=+ar%5E%28n-1%29 where a = the first term, and r is the common ratio
We are given 3rd and 6th terms:
a%283%29+=+ar%5E2+=+-75+-%3E+a+=+-75%2Fr%5E2
a%286%29+=+ar%5E5+=+-9375+-%3E+%28-75%2Fr%5E2%29r%5E5+=+-75r%5E3
Solve for r:
r%5E3+=+-9375%2F-75+=+125+-%3E+r+=+5
Since a%283%29+=+ar%5E2+=+a%285%29%5E2+=+-75 this means that the first term, a = -75/25 = -3
The rule for the nth term is a%28n%29+=+-3%2A5%5E%28n-1%29