Three numbers whose sum is 15 are successive terms of an arithmetic series. If 1,1 and 4 are added to these three numbers respectively, the resulting numbers are successive terms of a geometric series. Find the numbers.
I have found from using the sum that d=5−a
and from that deduced that the second term in the GP must be 6 (as T2=a+d+1) but where do I go from here?
Thanks!
Answer
Let the three numbers be 5−d,5,5+d
New numbers are 6−d,6,9+d are in G.P
Clearly 62=(9+d)(6−d)⇒d=3,−6
Original numbers are 2,5,8 or 11,5,−1.
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