Q. 95.0( 1 Vote )

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

Answer :

Let the first term of G.P be .

second term = a and third term = ar.


(where, r is the common ratio)


sum of three terms is 156



a3 = 216


a = 6. ……..(1)


Also,sum of their product in pairs is 216.



………(2)


Substituting (1) in (2), we get-



36(1 + r + r2) = 156r


36 + 36r + 36r2 = 156r


36 -120r + 36r2 = 0


12(3r2-10r + 3) = 0


3r2-10r + 3 = 0


3r2-9r-1r + 3 = 0


3r(r-3) -1(r-3) = 0


(3r-1)(r-3) = 0



Now, G.P will be-





18, 6, 2 or 2, 6, 18 are the three consecutive terms.


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