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

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise
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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 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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