# If a

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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