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.

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) (Show Source): You can put this solution on YOUR website!
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:

where a = the 1st term, r = the common ratio
Given: a_3 = -75, a_6 = -9375
So we have two equations:

From the 1st equation we have

Substituting this into the equation for a_6 gives

This gives r = 5
Use the formula for a_3 above to solve for a:

This gives a = -3
So the rule for the nth term is:

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