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Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ a b c q r r p p q p1 qr q1 r p r1 pq qr r p pq A R A R A R pr pr q r rq r p pq pr p qr q q r r p p q A R A R 1 0 0 Thus, the given result is proved. Question 23: If the first and the terms, prove that P th n term of a G.P. are a and b , respectively, and if P ab 2 n Solution 23: The first term of the G.P is a Therefore, the G.P. is n b ar 1 ....... 1 P Product of n terms 2 n 1 aarar ...... ar 2 n 1 a a .... ar r .... r n 1 2 .... n a r 1 ....... 2 Here, 1,2,..... n 1 1 2 ....... n 1 . and the last term is b . a, ar, ar , ar .... ar is an A.P. 2 3 n 1 , where r n1 n1 n n1 2 n 1 1 1 2 n 2 2 2 2 P nn1 n 2 a r P a r 2 2n nn1 n 2 n 1 a r 1 n is the common ratio. is the product of n n aar n ab Using 1 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 24: Show that the ratio of the sum of first n 2 th n term is 1/ r n . Solution 24: Let a be the first term and r be the common ratio of the G.P. Sum of first n Since there are n terms Sum of terms from n an 1 1 r Sn 1 r a ar ar n1 n<strong>11</strong> n Thus, required ratio a 1 r 1 r terms from n 1 th n n 1 th to 2 th n terms of a G.P. to the sum of terms from to term 2 th n a 1 r 1 r 1 n n n 1 r ar 1 r r Thus, the ratio of the sum of first n n term is 1/ r . n term, terms of a G.P. to the sum of terms from n 1 th n 1 th to to 2 th n Question 25: If abc , , and d are in G.P. show that: a 2 b 2 c 2 b 2 c 2 d 2 ab bc cd 2 Solution 25: If and d are in G.P. Therefore, abc , , bc ad ........ 1 2 b ac........ 2 c 2 bd ......... 3 It has to be proved that, a 2 b 2 c 2 b 2 c 2 d 2 ab bc cd 2 R.H.S. ab bc cd 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 1 - Sets Maths ___
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Class XI Chapter 2 - Relations and
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Class XI Chapter 3 - Trigonometric
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Class XI Chapter 4 - Principle of M
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Class XI Chapter 5 - Complex Number
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Class XI Chapter 6 - Linear Inequal
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Class XI Chapter 7 - Permutation an
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 10 - Straight Line
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Class XI Chapter 11 - Conic Section
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Class XI Chapter 12 - Introduction
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Class XI Chapter 13 - Limits and De
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Class XI Chapter 14 - Mathematical
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Class XI Chapter 15 - Statistics Ma
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