Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 2 2 ab m n n Adding (1) and (2), we obtain a b .... 2 2 ab 2a m m n n 2 2 ab a m m n n 2 2 Substituting the value of a 2 ab ab b m m m n n n ab ab m m n n n ab m m n n 2 2 2 2 in (1), we obtain 2 2 ab m m n a m m n a: b n Thus, 2 2 2 2 b ab 2 2 2 2 m m n n m m n a : b m m n : m m n 2 2 2 2 Question 20: If abc , , are in A.P; Solution 20: It is given that b a c b It is given that c 2 bd abc , , b, c, d b, c, d ...... 2 Also, 1 , 1 , 1 are in A.P. c d e 1 1 1 1 d c e d are in G.P. and 1 , 1 , 1 c d e are in A.P. ...... 1 are in G.P. are in A.P. prove that a,, c e are in G.P. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 1 1 d c e ...... 3 It has to be proved that a,, c e are in G.P. i.e., From (1), we obtain 2b a c a c b 2 From (2), we obtain 2 c d b Substituting these values in (3), we obtain 2b 1 1 2 c c e 2 a c 1 1 2 2c c e a c e c 2 c ce a c e c c e a ce e cc 2 ae ce ec c 2 c Thus, ae ac , and e are in G.P. 2 c ae Question 21: Find the sum of the following series up to n terms: (i) 5 55 555 .... (ii) .6 .66 .666 ... Solution 21: (i) 555 555 .... Let S n 5 55 555 ....to n terms 5 9 99 999 .....to n terms 9 2 3 5 10 1 10 1 10 1 ...to n terms 9 2 3 5 10 10 10 to n terms 1 1 ...to n terms 9 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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