Question
which number should be subtracted from each of the three numbers 5, 15, and 50 so that the resulting three numbers form a geometric progression?
Answers
Steve
we want the ratio between consecutive terms to be constant:
(15-x)/(5-x) = (50-x)/(15-x)
(15-x)(15-x) = (50-x)(5-x)
x^2 - 30x + 225 = x^2 - 55x + 250
25x = 25
x = 1
Check
4,14,49 form a GP where r=7/2
(15-x)/(5-x) = (50-x)/(15-x)
(15-x)(15-x) = (50-x)(5-x)
x^2 - 30x + 225 = x^2 - 55x + 250
25x = 25
x = 1
Check
4,14,49 form a GP where r=7/2