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If a, b and c are in A.P., a, x, b are in G.P. whereas b, y and c are also in G.P. Show that x2, b2, y2are in A.P.
Asked by ourrishita | 16 Feb, 2019, 03:29: PM
if a, b and c are in A.P., then 2b = (a+c) .......................(1)

if a, x and b are in G.P., then ab = x2 ............................(2)

if b,y and c are in G.P., then bc = y2  .........................(3)

by adding (2) and (3), we get,   ab + bc = b(a+c) = x2 + y2   ....................(4)

using eqn. (1) in eqn.(4), we get,  2b2 = x2 + y2  .........................(5)

from eqn.(5), we know that, x2 , b2 and y2 are in A.P.,
Answered by Thiyagarajan K | 16 Feb, 2019, 08:07: PM

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