Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 4n 1 n 3 2 12 1 n n n 3 Miscellaneous Exercise Question 1: Show that the sum of th Solution 1: Let a and d that the th k a a k 1 d k m n and th m n terms of an A.P. is equal to twice the th m term. be the first term and the common difference of the A.P. respectively. It is known term of an A.P. is given by a a m n 1 d mn a a m n 1 d m n a a m 1 d m mn mn 1 1 a a a m n d a m n d 2a m n 1 m n 1 d 2a 2m 2 d 2a 2 m 1 d 2a m 1 d 2a m Thus, the sum of m n th and m n th terms of an A.P. is equal to twice the th m term. Question 2: Let the sum of three numbers in A.P., is 24 and their product is 440, find the numbers. Solution 2: Let the three numbers in A.P. be a d, a, and a d. 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 ______________________________________________________________________________ According to the given information, a d a a d 24 ...... 1 3a 24 a 8 a d a a d 440 ...... 2 d d 8 8 8 440 d d 8 8 55 2 64 d 55 2 d d 2 64 55 9 3 d 3, the numbers are 5, 8 and **11** and when Therefore, when and 5. Thus, the three numbers are 5, 8 and **11**. d 3, the numbers are **11**, 8 Question 3: Let the sum of S 3 S S 3 2 1 Solution 3: Let a and b n S1 2a n 1 d 2 n, 2 n,3n terms of an A.P. be S1, S2 and S 3 , respectively, show that be the first term and the common difference of the A.P. respectively. Therefore, …….. (1) 2n S2 2a 2n 1 d n 2a 2n 1 d ....... 2 2 3n S3 2a 3n 1 d ....... 3 2 From (1) and (2), we obtain n S2 S1 n 2a 2n 1 d 2a n 1 d 2 4a 4nd 2d 2a nd d n 2 2a 3nd d n 2 n 2a 3n 1 d 2 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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