Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 ab ad cd Using 1 2 ab d a c 2 2 2 2 a b 2abd a c d a c a b 2a bd 2acbd d a 2ac c 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a b 2a c 2b c d a 2 d b d c [Using 1 and 2 ] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a b a c a c b c b c d a d b d b d c 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a b a c a d b b b c b d c b c c c d [Using (2) and (3) and rearranging terms] a b c d b b c d c b c d 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a b c b c d L.H.S R.H.S. L.H.S 2 2 2 2 2 2 2 a b c b c d ab bc cd Question 26: Insert two numbers between 3 and 81 so that the resulting sequence is G.P. Solution 26: Let G 1 and be two numbers between 3 and 81 such that the series, 3, Let a be the first term and r be the common ratio of the G.P. G 2 3 81 3 r r 3 27 r 3 (Talking real roots only) For r 3, G1 ar 3 3 9 G 2 ar 2 2 3 3 27 Thus, the required two numbers are 9 and 27. G, G ,81 1 2 , forms a 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 ______________________________________________________________________________ Question 27: Find the value of n Solution 27: M. of a and b is so that ab By the given condition: a a a a n1 n1 n b b n1 n1 n b b Squaring both sides, we obtain a 2 n1 n 1 a n b b n 2 ab n n may be the geometric mean between a ab a 2a b b ab a 2a b b 2n2 n1 n1 2n2 2n n n 2n a 2a b b a b 2a b ab 2n2 n1 n1 2n2 2n1 n1 n1 2n1 a b a b ab 2n2 2n2 2n1 2n1 a a b ab b 2n2 2n1 2n1 2n2 2 n 1 2n1 a a b b a b 2n1 0 a a 1 b b 2n 1 0 n 1 2 and b . Question 28: The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio 3 2 2 : 32 2 Solution 28: Le the two numbers be a and b . G.M. According to the given condition, ab a b 6 ab ...... 1 a b 2 36ab Also, 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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