Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Question 15: The p th , q th and b p qc 0 th r terms of an A.P. are abc , , respectively. Show that q r a r p Solution 15: Let t and d be the first term and the common difference of the A.P. respectively. The th n term of an A.P. is given by, Therefore, a t p 1 d a ........ 1 p a t q 1 d b ........ 2 q r 1 ........ 3 a t r d c Subtracting equation (2) from (1), we obtain p 1 q 1 d a b p q d a b a b d p q ...... 4 Subtracting equation (3) from (2), we obtain q 1 r 1 d b c q r d b c b c d q r ...... 5 Equating both the values of d a b b c p q q r a b q r b c p q aq bq ar br bp bq cp cq bp cp cq aq ar br aq ar bp br cp cq 0 a q r br p c p q 0 a q r br p c p q 0 Thus, the given result is proved. a t n 1 d n obtained in (4) and (5), we obtain 0 (By rearranging terms) 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 16: If 1 1 1 1 1 1 a , b , c b c c a a b Solution 16: It is given that a are in A.P., prove that 1 1 1 1 1 1 a , b , c b c c a a b 1 1 1 1 1 1 1 1 b a c b c a b c a b c a b a c a b c c a b b a c ac bc ab ac 2 2 2 2 2 2 2 2 b a b c a b a c c a c b b a b c abc abc 2 2 2 2 2 2 2 2 b a a b b c a c c a b a c b b c 2 2 2 2 ab b a c b a a c b bc c b are in A.P. ab b a c b a b a a c b c b bc c b b aab cb ca c bac ab bc ba c b Thus, and c are in A.P. ab , abc , , are in A.P. Question 17: If a, b, c, d Solution 17: It is given that b c 2 ad 2 ac bd bc are in G.P., prove that abc , , ...... 1 ........ 2 ...... 3 and d are in G.P. a b , b c , c d n n n n n n It has to be proved that n n 2 n n n n b c a b , c d Consider L.H.S. 2 2 2 b c b 2b c c n n n n n n a b , b c , c d n n n n n n are in G.P. i.e., are in G.P. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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