Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ n 2 1 1 1 2 a n d 5n 4 n 2a 9 6 2 n 1 n d 2 2 2a1 n 1 d1 5n 4 2a n 1 d 9n 5 2 2 Substituting 2 2 ....... 1 n 35 in (1), we obtain 2a 5 35 4 1 34d 1 2a 34d 9 35 6 a1 17d1 179 a 17d 321 2 2 ....... 2 th 18 termof first a 17d th 18 termof second A.P. a 17d From (2) and (3), we obtain th 18 termof first 179 th 18 termof second A.P. 321 1 1 2 2 …….. (3) Thus, the ratio of 18 th term of both the A.P.s is 179 : 321. Question 10: If the sum of first of the first Solution 10: p q p terms of an A.P. is equal to the sum of the first q terms, then find the sum terms. Let a and d be the first term and the common difference of the A.P. respectively. Here, p SP 2a p 1 d 2 b p Sq 2a q 1 d 2 According to the given condition, p q 2a p 1 d 2a q 1 d 2 2 p 2a p 1 d q 2a q 1 d 2ap pd p 1 2aq qd q 1 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 ______________________________________________________________________________ 2a p q d p p 1 q q 1 0 2 2 2a p q d p p q q 0 2a p q d p q p q p q 0 2a p q d p q p q 1 0 2a d p q 1 0 2a d pq1 ...... 1 p q S pq 2a p q 1 d 2 p q 2a S pq 2a p q 1 2 pq1 p q 2 0 2a2a p q Thus, the sum of the first terms of the A.P is 0. [From (1)] Question **11**: Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a b c p q r q r r p p q 0 Solution **11**: Let a 1 and d be the first term and the common difference of the A.P. respectively. According to the given information, p S p 2a1 p 1 d a 2 2a 2a1 p 1 d ....... 1 p q Sq 2a1 q 1 d b 2 2b 2a1 q 1 d ...... 2 q r Sr 2a1 r 1 d c 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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