Q. 105.0( 1 Vote )

Find the first three consecutive terms in G.P. whose sum is 7 and the sum of their reciprocals is

Answer :


second term = a and third term = ar.


(where, r is the common ratio)


sum of three terms is 7



……..(1)





………(2)


Now, R.H.S of equation (1) & (2) is equal-


L.H.S of equation (1) = L.H.S of equation (2)



a2 = 4


a = √4


a = 2


Now substituting a = 1 in (2), we get-



2 + 2r + 2r2 = 7r


2r2-5r + 2 = 0


2r2-4r-r + 2 = 0


(2r-1)(r-2) = 0



Now, G.P will be-





4, 2, 1 or 1, 2, 4 are the three consecutive terms.


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