Question

The second,third and sixth terms of A.P. are consecutive terms of a geometric progression. Find the common ratio of the geometric progression​

Answer 1

Answer:

answered Jul 15 by kavitaKumari (11.9k points) Given: Second, third and sixth terms of an A.P. are consecutive terms of a G.P. Let the first term of AP be a and the common difference be d. ⇒ An = a+(n-1)d ⇒ A2 = a+d ⇒ A3 = a+2d ⇒ A6 = a+5d If a,b,c are consecutive terms of GP then we can write b2 = a.c ∴ We can write (a+2d)2 = (a+d).(a+5d) ⇒ a2+4d2+4ad = a2+6ad+5d2 ⇒ d2+2ad = 0 ⇒ d(d+2a) =0 ∴ d = 0 or d =-2a When d = 0 then the GP becomes a,a,a. ∴ The common ration becomes 1. When d = -2a then the GP becomes –a, -3a,-9a ∴ The common ratio becomes 3Read more on Sarthaks.com - https://www.sarthaks.com/1152884/if-second-third-and-sixth-terms-of-an-are-consecutive-terms-of-write-the-common-ratio-of-the