Q14 of 110 Page 48

If a, b, c, d are in a geometric sequence, then show that (a - b + c) (b + c + d) = ab + bc + cd.

Proof:∵ a, b, c, d are in G.P


⇒ a = a, b = ar, c = ar2,d = ar3.


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


= a2r (1 + r2 + r4 )


And, R.H.S = a2r + a2r3 + a2r5


= a2r (1 + r2 + r4 )


⇒ L.H.S = R.H.S


Hence, proved that-


(a - b + c) (b + c + d) = ab + bc + cd.


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