Check sibling questions

Example 5 - Find a if the 17th and 18th terms of (2 + a)^50 are equal

Example  5 - Chapter 8 Class 11 Binomial Theorem - Part 2
Example  5 - Chapter 8 Class 11 Binomial Theorem - Part 3

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Transcript

Example 5 Find a if the 17th and 18th terms of the expansion (2 + a)50 are equal. We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br Finding 17th term T17 = T16 + 1 of (2 + a)50 Putting r = 16, n = 50, a = 2 and b = a in (1) T16 + 1 = 50C16 (2)50 – 16 . (a)16 T17 = 50C16 . (2)34 . a16 Finding 18th term T18 = T17+1 of (2 + a)50 Putting r = 17, n = 50, a = 2 and b = a in (1) T17+1 = 50C17 (2)50 – 17 . (a)17 T18 = 50C17 (2)33. (a)17 Now it is given that 17th term = 18th term 50C16 (2)34 . (a)16 = 50C17 (2)33 . a17 ("50C16 " . 234)/("50C17 ." 233" " ) = 𝑎17/𝑎16 "50C16" /"50C17 " . (2)34 – 33 = a "50C16" /"50C17 " × 21 = a (50!/16!(50 −16)!)/(50!/17!(50−17)!) × 2 = a 50!/(16! × 34!) × (17! × 33!)/50! × 2 = a (17 × 16! × 33!)/(16! × 34 × 33!) × 2 = a 17/34 × 2 = a 17/17 = a a = 1 Hence, a = 1

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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.