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BITSAT2021MathematicsSequences and SeriesActual

If the sum of a certain number of terms of the A.P. 25,22,19, is 116 then the last term is

Options

  1. A0
  2. B2
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

a=25, d=22-25=-3 . Let n be the no. of terms array l Sum =116 ; Sum = n 2 [2 a+(n-1) d] 116= n 2 [50+(n-1)(-3)] or 232=n[50-3 n+3]=n[53-3 n]=-3 n²+53 n 3 n²-53+232=0 (n-8)(3 n-29)=0 n=8 or n= 29 3 , n 29 3 n=8 Now, T ₈=a+(8-1) d=25+7 (-3)=25-21=4 Last term =4 array

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