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BITSAT2022MathematicsSequences and SeriesActual

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2 . If the middle term of AP be equal to the middle term of the GP , then the middle term of the entire sequence is

Options

  1. A- 10 31
  2. B10 31
  3. C32 31
  4. D- 31 32

Correct answer

A. - 10 31

Step-by-step solution

Since, the first 11 terms are in AP , d=2 a₁₁=a+10 d=a+20 The middle term of AP is T₆=a+5 d=a+10 For the next 11 terms in GPr=2 The middle term of GP is b(2)^5 where, b is the first term of a GP which is the last term of APb(2)^5=(a+20) 32 According to the given condition, aligned a+10 & =(a+20) 32 31 a & =10-640 a & =- 630 31 aligned Middle term of entire sequence is 11th term aligned T₁₁ & = -630 31 +10 d & = -630 31 +10 2= -10 31 aligned

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