SOLUTION: Plese help me solve this geometric progression if 7,x,y,189 are in G.P Find x and y

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Question 1196576: Plese help me solve this geometric progression if 7,x,y,189 are in G.P Find x and y
Found 3 solutions by greenestamps, math_helper, ewatrrr:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The 4th term, 189, is the first term, 7, multiplied by the common ratio 3 times:

189=7r%5E3
r%5E3=189%2F7=27
r=3

The common ratio is 3; you can do the simple arithmetic to find x and y.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



7 = 7%2Ak%5E0

x = +7%2Ak%5E1

y = +7%2Ak%5E2

189 = +7%2Ak%5E3  -->  +k%5E3+=+189%2F7+=+27+ --> +k+=+root%283%2C27%29+ or +k=3+



x = 7%2A3%5E1 = 21

y = 7%2A3%5E2 = 7*9 = 63





So the progression is  7, 21, 63, 189, ...

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi


Geometric progression: {7,x,y,189}
a%5B1%5D+=+7  and a%5B4%5D+=189   |given
Need to Know!
a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29
 

a%5B4%5D+=+7%2Ar%5E%284-1%29
7r^3 = 189
or
r^3 = 27
r = 3

x = a%5B2%5D+=+7%2A3%5E%282-1%29+=+7%2A3%29 = 21
y= a%5B3%5D+=+7%2A3%5E%283-1%29+=+7%2A3%5E2 = 63

Wish You the Best in your Studies.