SOLUTION: Geometric sequences Write the first five terms of this geometric sequence. a1 = -64,fifth term is -4

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Question 924664: Geometric sequences
Write the first five terms of this geometric sequence.
a1 = -64,fifth term is -4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a%5B1%5D+=+-64,fifth term is a%5B5%5D=-4

a[n]=a[1]r^(n-1)...find r
a%5B5%5D=a%5B1%5Dr%5E%285-1%29
a%5B5%5D=a%5B1%5Dr%5E4
a%5B5%5D%2Fa%5B1%5D=r%5E4
-4%2F-64=r%5E4
1%2F16=r%5E4
r=root%284%2C1%2F16%29
r=root%284%2C1%5E4%2F2%5E4%29
r=1%2F2
so, formula is: a%5Bn%5D=a%5B1%5D%281%2F2%29%5E%28n-1%29
now we can find a%5B2%5D,a%5B3%5D, and a%5B4%5D
a%5B2%5D=-64%281%2F2%29%5E%282-1%29
a%5B2%5D=-64%281%2F2%29%5E1
a%5B2%5D=-64%2F2
a%5B2%5D=-32

a%5B3%5D=-64%281%2F2%29%5E%283-1%29
a%5B3%5D=-64%281%2F2%29%5E2
a%5B3%5D=-64%281%2F4%29
a%5B3%5D=-64%2F4
a%5B3%5D=-16
a%5B4%5D=-64%281%2F2%29%5E%284-1%29
a%5B4%5D=-64%281%2F2%29%5E3
a%5B4%5D=-64%281%2F8%29
a%5B4%5D=-64%2F8
a%5B4%5D=-8

now we can write the first five terms of this geometric sequence:

a%5B1%5D+=+-64
a%5B2%5D=-32
a%5B3%5D=-16
a%5B4%5D=-8
a%5B5%5D=-4