Check sibling questions

Ex 9.3, 23 - Chapter 9 Class 11 Sequences and Series (Term 1)

Last updated at Sept. 3, 2021 by

Ex 9.3, 23 - If first and nth term of GP are a and b - Geometric Progression(GP): Calculation based/Proofs

Ex 9.3, 23 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 23 - Chapter 9 Class 11 Sequences and Series - Part 3

This video is only available for Teachoo black users

Subscribe Now

Get Real time Doubt solving from 8pm to 12 am!

Join Teachoo Black now

Transcript

Ex 9.3, 23 If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab)n. Let a be the first term of G.P & r be the common ratio of G.P Given, first term of G.P = a We know that nth term of G.P = arn-1 b = arn-1 Now P is the product of n terms P = a1 a2 a3 an = a ar ar2 ar3 arn 1 = (a a a) (r r2 rn 1) = an ^(1+2+ +( 1)) = an ^(( ( 1))/2) Thus, P = an ^(( ( 1))/2) We need to prove P2 = (ab)n. Taking L.H.S P2 = ("an " r^((n(n 1))/2) )^2 = ( ^( 2) " " r^((n(n 1))/2 2) ) = ( ^2 " " r^(n(n 1)) ) = ( ^2 " " r^((n 1)) )^ = ( r^((n 1)) )^ = ( ( r^((n 1) )))^ = ( )^ = ( )^ = R.H.S Thus, P2 = ( )^ Hence proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.