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BITSAT2021MathematicsSequences and SeriesActual

The sum of all odd numbers between 1 and 1000 which are divisible by 3 is

Options

  1. A83667
  2. B90000
  3. C83660
  4. DNone of these

Correct answer

A. 83667

Step-by-step solution

Sum of odd numbers between 1 and 1000 , which is divisible by 3=3+9+15+21+27+ +999= S (let) Let n be the number of terms in series and a is first term. l=a+(n-1) d , where l is last term and d is is common difference. array l 999=3+(n-1) 6 n-1= 999-3 6 = 996 6 n-1=166 n=167 S = n 2 [2 a+(n-1) d] = 167 2 [2 3+(167-1) 6] = 167 2 [1002]=167 501=83667 array

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