Thursday, 20 August 2015

sequences and series - an AP is changed to form a GP



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=5a
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 5d,5,5+d




New numbers are 6d,6,9+d are in G.P



Clearly 62=(9+d)(6d)d=3,6



Original numbers are 2,5,8 or 11,5,1.


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