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Example 4 - In an AP if mth term is n, the nth term is m - Arithmetic Progression (AP): Calculation based/Proofs

Example 4 - Chapter 9 Class 11 Sequences and Series - Part 2
Example 4 - Chapter 9 Class 11 Sequences and Series - Part 3

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Example 4, In an A.P. if mth term is n and the nth term is m, where m n, find the pth term. We know that an = a + (n 1) d i.e. nth term = a + (n 1) d Thus, mth term = am = a + (m 1) d It is given that mth term is n a + (m 1) d = n Also, it is given that nth term is m a + (n 1) d = m First we find common difference, Subtracting (2) from (1) [a + (m 1) d] [a + (n 1) d] = n m a + (m 1)d a (n 1)d = n m a a + (m 1)d (n 1)d = n m (m 1)d (n 1)d = n m md d nd + d = n m md nd = n m d(m n) = n m d = ( )/( ) d = (( ) )/( ) 1 d = 1 Now we have to calculate a Putting d = 1 in (2) a + (n 1) d = m a + (n 1) (-1) = m a n + 1 = m a = m + n 1 For pth term, we use the formula, an = a + (n 1)d putting n = p, d = -1 and a = m + n 1 ap = (m + n 1) + ( p 1) ( 1) = m + n 1 + ( p + 1) = m + n 1 p + 1 = m + n p Thus, pth term = m + n p

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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.