Q. 155.0( 2 Votes )

If a, b, c, d are in a G.P., then prove that a + b, b + c, c + d, are also in G.P.

Answer :

Proof: a, b, c, d are in G.P


a = a, b = ar ,c = ar2,d = ar3.


To prove: a + b, b + c, c + d, are also in G.P, if-



(a + b) (c + d) = (b + c)2


Now, we need to prove : (a + b) (c + d) = (b + c)2


L.H.S. = (a + ar)(ar2 + ar3)


= a(1 + r) ar2 (1 + r)


= a2r2 (1 + r)2


R.H.S. = (ar + ar2)2


= (ar(1 + r))2


= a2r2 (1 + r)2


L.H.S = R.H.S


Hence, proved that-


(a + b) (c + d) = (b + c)2


a + b, b + c, c + d, are also in G.P


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