Sat February 19, 2011 By: Arun Iyer

Three numbers whose sum is 21 are in A P. If 2,2,14 are added to them respectively , the resulting numbers are in G P. Find the numbers.

Expert Reply
Sat February 19, 2011
Dear student,
Let the numbers in AP be a-d, a, a+d.
It is given that the sum of these numbers is 21.
So, a-d+a+a+d = 21
This gives, a = 7
So, the numbers are 7-d, 7, 7+d.
It is given that if 2, 2, 14 respectively are added to the numbers, then the resulting numbers are in GP.
So, 9-d, 9, 21+d are in GP.
Thus, when d = -18, the numbers are 25, 7, -11.
When d = 6, the numbers are 1, 7, 13
We hope that clarifies your query.
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