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

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Question 493683: the third and sixth terms of a geometric sequence are-75 and -9375 respectively. Find the first term, common ratio, and an explict rule for the nth term.
Answer by htmentor(1343) About Me  (Show Source):
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the third and sixth terms of a geometric sequence are-75 and -9375 respectively. Find the first term, common ratio, and an explict rule for the nth term.
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The general formula for the n-th term of a geometric sequence is:
a_n+=+a%2Ar%5E%28n-1%29
where a = the 1st term, r = the common ratio
Given: a_3 = -75, a_6 = -9375
So we have two equations:
a_3+=+-75+=+a%2Ar%5E2
a_6+=+-9375+=+a%2Ar%5E5
From the 1st equation we have
a+=+-75%2Fr%5E2
Substituting this into the equation for a_6 gives
-9375+=+%28-75%2Fr%5E2%29%2Ar%5E5
r%5E3+=+125
This gives r = 5
Use the formula for a_3 above to solve for a:
-75+=+a%2A5%5E2
This gives a = -3
So the rule for the nth term is:
a_n+=+-3%2A5%5E%28n-1%29