SOLUTION: If 8,x,y and 27 are four consecutive terms of a G.P, find the value of x and y.

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Question 1126559: If 8,x,y and 27 are four consecutive terms of a G.P, find the value of x and y.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


recall: In a Geometric Sequence each term is found by multiplying the previous term by a constant (common ratio r).
We can also calculate any term using the Rule:
a%5Bn+%5D=+a%5B1%5D%2Ar%5E%28n-1%29
If 8,x,y, 27, we know that
a%5B1%5D=8
a%5B2%5D=x
a%5B3%5D=y
a%5B4%5D=27
use first and fourth term, plug it in a%5Bn+%5D=+a%5B1%5D%2Ar%5E%28n-1%29 to find common ratio r
27=+8%2Ar%5E%284-1%29
27%2F8=r%5E3
r%5E3=27%2F8
r%5E3=%283%2F2%29%5E3
r=3%2F2
now find second term:
a%5Bn+%5D=+a%5B1%5D%2Ar%5E%28n-1%29...n=2
a%5B2%5D=+8%2A%283%2F2%29%5E%282-1%29
a%5B2%5D=+8%2A%283%2F2%29
a%5B2%5D=+4%2A3
a%5B2%5D=+12 ->+x=12

now find third term:
a%5Bn+%5D=+a%5B1%5D%2Ar%5E%28n-1%29...n=3

a%5B3%5D=+8%2A%283%2F2%29%5E%283-1%29}}}
a%5B3%5D=+8%2A%283%2F2%29%5E2
a%5B3%5D=+8%2A%289%2F4%29
a%5B3%5D=+2%2A9
a%5B3%5D=+18 ->y=18

double check the fourth term:
a%5B4%5D=+8%2A%283%2F2%29%5E%284-1%29
a%5B4%5D=+8%2A%283%2F2%29%5E3
a%5B4%5D=+8%2A%2827%2F8%29
a%5B4%5D=+27 -> as given

so, the value of x=12 and y=18