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Question

If the product of three consecutive term in G.P is 216 and sum of their products in pairs is 156, find them.

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Solution

Let ar,a ar be three consecutive term in G.P.
with common ratio 'r'
then according to question
ar×a×ar=216 ------ (1)
a3=216
[a=6]
and
a2r+a2r+a2=156
a2[1r+r+1]=156
r2+r+1r=15636
3r2+3r+3=13r
3r210r+3=0
3r29rr+3=0
(3r-1)(r-3)=0
r=13 or r=3
three numbers are 18,6,2 or 2,6,18.

1208253_1362141_ans_9740f742c6414c158b41f0dae6cd9515.JPG

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