Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2c 2a1 r 1 d ...... 3 r Subtracting (2) from (1), we obtain 2a 2b p 1 d q 1 d p q 2aq 2bp d p 1 q 1 pq 2aq 2bp d p q pq 2 aq bp d pq p q ...... 4 Subtracting (3) from (2), we obtain 2b 2c q 1 d r 1 d q r 2b 2c d q 1 r 1 q r 2br 2qc d q r qr 2 br qc d qr q r ...... 5 Equating both the values of d obtained in (4) and (5), we obtain aq bp br qc pq p q qr q r qr q raq bq pq q qbr qc r aq bpq r p br qc p q aqr bprq r bpr pqc p q Dividing both sides by pqr, we obtain a b b c p q q r q r p q a b c q r q r p q p q p q r 0 a b c p q r q r r p p q 0 Thus, the given result is proved. 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 12: The ratio of the sums of m and n terms of an A.P. is 2m1 : 2n1 term is . m : n 2 2 . Show that the ratio of Solution 12: Let a and b be the first term and the common difference of the A.P. respectively. According to the given condition, Sumof mterms m Sumof nterms n m 2 a m 1 d m 2 n 2a n 1 d 2 2a m 1 d m 2a n 1 d n Putting m2m1 2 2 and 2a 2m 2 d 2m 1 2a 2n 2 d 2n 1 a m 1 d 2m 1 a n 1 d 2n 1 n 2 2 ....... 1 n2n1 th m termof A.P. a m 1 d th n termof A.P. a n 1 d From (2) and (3), we obtain m n th th termof A.P. 2m1 termof A.P. 2n1 Thus, the given result is proved. , we obtain …….. (2) ...... 3 th m and th n Question 13: If the sum of n terms of an A.P. of and its Solution 13: Let a and b be the first term and the common difference of the A.P. respectively. a a m 1 d 164 ...... 1 m Sum of n terms: 2 1 2 3n 5 n Sn a n d 2 n th m term is 164, find the value of m. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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