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

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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