SOLUTION: Find a number x which, when added to each of the numbers 21, 27, and 29 in this order, produces three numbers which are in a geometric progression.

Question 1043415: Find a number x which, when added to each of the numbers 21, 27, and 29 in this order, produces three numbers which are in a geometric progression.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
21, 27, 29
:
use the definition for any term in a geometric progression
:
an = a0 * r^(n-1)
:
a0 = 21+x
:
1) a1 = 27+x = (21+x) * r
2) a2 = 29+x = (21+x) * r^2
:
solve equation 1 for r
:
r = (27+x) / (21+x)
:
substitute for r in equation 2
:
29+x = (21+x) * (27+x)^2 / (21+x)^2
:
29+x = (27+x)^2 / (21+x)
:
(29+x)*(21+x) = (27+x)^2
:
x^2 +50x +609 = x^2 +54x +729
:
4x = -120
:
x = -30
:
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we add -30 to each number
-9, -3, -1
the common ratio is 1/3
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