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Ex 9.2, 10 - If sum of first p terms of AP is equal to - Ex 9.2

Ex 9.2, 10 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.2, 10 - Chapter 9 Class 11 Sequences and Series - Part 3
Ex 9.2, 10 - Chapter 9 Class 11 Sequences and Series - Part 4
Ex 9.2, 10 - Chapter 9 Class 11 Sequences and Series - Part 5

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Ex9.2 , 10 If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms. We know that Sn = n/2 ( 2a + (n 1)d ) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Now, Sum of first p terms = Sp = p/2 [2a + (p 1)d] Sum of first q terms = Sq = q/2 [2a + (q 1)d] It is given that Sum of first p terms = Sum of first q terms p/2 [2a + (p 1)d] = q/2 [2a + (q 1)d] p[2a + (p 1)d] = (2 )/2[2a + (q 1)d] p[2a + (p 1)d] = q[2a + (q 1)d] 2ap + pd(p 1) = 2aq + qd (q 1) 2ap 2aq = qd (q 1) pd(p 1) 2a(p q) = d[(q 1)q (p 1)p] 2a(p q) = d[q2 q (p2 p)] 2a(p q) = d[q2 q p2 + p] 2a(p q) = d[q2 p2 + p q] 2a(p q) = d [ q2 + p2 p + q] 2a(p q) = d [p2 q2 (p q)] 2a(p q) = d [(p q) (p + q) (p q)] 2a(p q) = d(p q) [p + q 1] 2a(p q) + d(p q) [p + q 1] = 0 (p q) [2a + d(p + q 1)] = 0 2a + d(p + q 1) = 0 Now, finding sum of first (p + q) terms We know that, Sum of n terms = n/2 [2a + (n 1)d] For sum of (p + q) terms, we put n = (p + q) Sum of (p + q) term is = (p + q)/2 [2a + (p + q 1)d] = (p + q)/2 0 = 0 Hence, sum of (p + q) term is 0

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.