SOLUTION: Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

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Question 697063: Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Substitute 21 for a2 and 567 for a5 in the formula

an+=+a1%2A+r%5E%28n-1%29

a2=+a1%2A+r%5E%282-1%29...-> ..a1%2Ar=21

a5=+a1%2A+r%5E%285-1%29...->..+a1%2Ar%5E4=567

Substitute this expression for a1 in the second equation and solve for r.

a1+=21%2Fr

a1%2Ar%5E4=567

%2821%2Fr%29%2Ar%5E4=567

21%2Ar%5E3=567

r%5E3=567%2F21

r%5E3=27

r=3

Substitute for r in the first equation and solve for a1.

a1%2A+r=21

a1%2A3=21

a1+=21%2F3

a1+=7

Now use the formula to find the nth term an.

highlight%28an=+7%2A3%5E%28n-1%29%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

r = -+3

a%5B1%5D+=+%28-+21%29%2Fr+

a%5B1%5D+=+%28-+21%29%2F-+3, or 7 ----- Substituting – 3 for r

Therefore, equation for the nth term = highlight_green%28a%5Bn%5D+=+a%5B1%5D%28-+3%29%5E%28n+-+1%29%29, or highlight_green%28a%5Bn%5D+=+7%28-+3%29%5E%28n+-+1%29%29