SOLUTION: Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively choices below an = 7 • (-3)n + 1 an = 7 • 3n - 1

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Question 1135564: Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively
choices below
an = 7 • (-3)n + 1

an = 7 • 3n - 1

an = 7 • (-3)n - 1

an = 7 • 3n
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n+-+1+%29
if the second and fifth terms are +a%5B2%5D+=-21 and +a%5B5%5D+=567, respectively
-21+=+a%5B1%5D%2Ar%5E%282+-+1+%29
-21+=+a%5B1%5D%2Ar......solve for a%5B1%5D
a%5B1%5D=-21%2Fr.......eq.1


567+=+a%5B1%5D%2Ar%5E%285+-+1+%29
567+=+a%5B1%5D%2Ar%5E4......solve for a%5B1%5D
a%5B1%5D=567%2Fr%5E4.......eq.2

from eq.1 and eq.2 we have

567%2Fr%5E4=-21%2Fr
567%2Fr%5E3=-21
r%5E3=567%2F-21
r%5E3=-27
r%5E3=-3%5E3
highlight%28r=-3%29

now find first term
a%5B1%5D=-21%2F-3.......eq.1
highlight%28a%5B1%5D=7%29

so, your ormula is:
a%5Bn%5D+=7%2A%28-3%29%5E%28n-1%29