Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Here, n 2a nd d 3n 5n 2 2 d nd 2 2 2 2 na n 3n 5n Comparing the coefficient of 2 n on both sides, we obtain d 3 2 d 6 Comparing the coefficient of n on both sides, we obtain d a 5 2 a 3 5 a 8 Therefore, from (1), we obtain 8 m 1 6 164 m 1 6 164 8 156 m1 26 m 27 Thus, the value of m is 27. Question 14: Insert five numbers between 8 and 26 such that resulting sequence is an A.P. Solution 14: Let A1 , A2 , A3 , A 4 and A 5 be five numbers between 8 and 26 such that 8, A1 , A2 , A3 , A4 , A 5,26 is an A.P. Here, Therefore, a 8, b 26, n 7 6d 26 8 18 d 3 26 8 7 1 d A1 a d 83 **11** A2 a 2d 8 23 86 14 A3 a 3d 833 89 17 A4 a 4d 8 43 812 20 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 ______________________________________________________________________________ A5 a 5d 8 53 815 23 Thus, the required five numbers between 8 and 26 are **11**, 14, 17, 20 and 23. Question 15: n n a b If is the A.M. between a and b, then find the value of n. n1 n1 a b Solution 15: A.M. of a and b a b 2 According to the given condition, n a b a b 2 a b n n1 n1 n1 n1 n n a ba b 2a b a ab ba b 2a 2b n n1 n1 n n n ab a b a b n1 n1 n n n1 n n n1 ab b a a b n b n1 1 b a b a a b a n1 n1 n1 0 a a 1 b b n 1 0 n 1 Question 16: Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7 th and numbers is 5:9. Find the value of m. Solution 16: m 1 th Let A1, A2,..... A m be m numbers such that 1, A1, A2,..... A m,31 is an A.P. Here, a 1, b 31, n m 2 m d m d 31 1 2 1 30 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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