SOLUTION: If a5= 48 and a17=196608 are he terms of a geometric sequence find a32.. Please help me solve this geometric sequence.

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Question 524216: If a5= 48 and a17=196608 are he terms of a geometric sequence find a32.. Please help me solve this geometric sequence.
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Formula to find nth geometric term a%5Bn%5D=a%5B1%5D%2Ar%5En-1
a%5Bn%5D = nth term
a%5B1%5D = First term
r = Common ratio
n = number of term




a%5B5%5D=48
48=a%5B1%5D%2Ar%5E%285-1%29
48=a%5B1%5D%2Ar%5E4%29
a%5B1%5D%2Ar%5E4=48%29
a%5B1%5D=48%2Fr%5E4%29...............(1)
a%5B17%5D=196608
196608=a%5B1%5D%2Ar%5E%2817-1%29
196608=a%5B1%5D%2Ar%5E16
a%5B1%5D=196608%2Fr%5E16...........(2)

a%5B1%5D=a%5B1%5D

48%2Fr%5E4=196608%2Fr%5E16%29
r%5E16%2Fr%5E4=196608%2F48%29
r%5E%2816-4%29=4096%29
r%5E12=4096%29
r%5E12=%282%29%5E12%29
r=2%29
Put the value of r in (1)
a%5B1%5D=48%2F2%5E4%29
a%5B1%5D=48%2F16
a%5B1%5D=3

Put the value of a%5B1%5D and r in the formula for finding nth term in our case it is a%5B32%5D
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B32%5D=3%2A%282%29%5E%2832-1%29
a%5B32%5D=3%2A2%5E31
a%5B32%5D=%283%2A2147483648%29
a%5B32%5D=6442450944