Q13 of 104 Page 468

If a, b, c are in GP, prove that a2, b2, c2 are in GP.

To prove: a2, b2, c2 are in GP


Given: a, b, c are in GP


Proof: As a, b, c are in GP


⇒ b2 = ac … (i)


Considering b2, c2


= common ratio = r


⇒ [From eqn. (i)]


⇒ = r


Considering a2, b2


= common ratio = r


⇒ [From eqn. (i)]


⇒ = r


We can see that in both the cases we have obtained a common ratio.


Hence a2, b2, c2 are in GP.


More from this chapter

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11

If a, b, c, d are in GP, prove that

(i) (b + c)(b + d) = (c + a)(c + a)


(ii)


(iii) (a + b + c + d)2 = (a + b)2 + 2(b + c)2 + (c + d)2


 12

If a, b, c are in GP, prove that are in AP.

 14

If a, b, c are in GP, prove that a3, b3, c3 are in GP

 15

If a, b, c are in GP, prove that (a2 + b2), (ab + bc), (b2 + c2) are in GP.