Three numbers form a G.P. If the 3rd term is decreased by 64, then the three numbers thus obtained will constitute an A.P. If the second term of this A.P. is decreased by 8, a G.P. will be formed again. Determine the numbers.
Open in App
Solution
Let a,ar,ar2 are in G.P Then, a,ar,ar2−64 are in A.P ∴2ar=a+ar2−64, or a(r2−2r+1)=64.......(1) Again a,ar−8,ar2−64 are in G.P. ∴(ar−8)2=a(ar2−64) or −16ar+64=−64a or a(16r−64)=64........(2) ∴r2−2r+1=16r−64 [by (1) and (2)] or r2−18r+65=0 ∴(r−5)(r−13)=0∴r=5, hence a=4, ∴ Number are 4,20,100 which are in G.P..