Q15 of 110 Page 48

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

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


More from this chapter

All 110 →
13

A company purchases an office copier machine for ₹50,000. It is estimated that the copier depreciates in its value at a rate of 15% per year. What will be the value of the copier after 15 years?

 14

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

 1

Find the sum of the first (i) 75 positive integers (ii) 125 natural numbers.

 2

Find the sum of the first 30 terms of an A.P. whose nth term is 3 + 2n.