Q10 of 110 Page 48

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


⇒ 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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