Let the three numbers of the GP be a,ar and ar2 where r is the common ratio.
According to the given condition, a,2ar and ar2 are in AP.
∴2ar=2a+ar2
∴a+ar2=4ar
∴r2+1=4r
∴r2−4r+1=0
∴r=24±16−4
=24±23=2±3
As it is an 'increasing' GP, r>1.
∴r=2+3.
Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :
Held on 6 Apr 2014 · Verified 6 Jul 2026.
2−3
2+3
2+3
3+2
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