Question

plz prove it urgent.............

Answer 1

(6)

∴ If a,b,c,d are in GP then there should be a real number r such that:

⇒ a

⇒ b = ar

⇒ c = ar²

⇒ d = ar³

Since a,b,c,d are in GP. Therefore,

⇒ b/a = r then, b = ar.

⇒ c/b = r then, c = br.

⇒ d/c = r then, d = cr.

Now,

Given (a + b),(b + c),(c + d) are in GP.

(i)

⇒ a + b

⇒ a + ar

⇒ a(1 + r).

(ii)

⇒ b + c

⇒ ar + ar²

⇒ ar(1 + r)

(iii)

⇒ c + d

⇒ ar² + ar³

⇒ ar²(1 + r).

In all cases, the common ratio is r.

Therefore, (a + b),(b + c) and (c + d) are in GP.

Hope it helps!