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AP EAMCET202017 Sep 2020Evening ShiftMathematicsSequences and SeriesActual

If (x= 1 5 + 1 3 5 10 + 1 3 5 5 10 15 + ). then (3 x^2+6 x= )

Options

  1. A1
  2. B2
  3. C-1
  4. D-2

Correct answer

B. 2

Step-by-step solution

We have, (x= 1 5 + 1 3 5 10 + 1 3 5 5 10 15 + ) Comparing expression with, ((1+y)^n= 1+n y 1 ! + n(n-1) 2 ! y^2+ . ) we get, (n y= 1 5 , n(n-1) 2 1 y^2= 1 3 5 10 ) Solving we get, (y=- 2 5 and n=- 1 2 ) So, ( array ll x=(1+y)^n-1 & x= (1- 2 5 )^ - 1 2 -1= 5 3 -1 array ) So, ( 3 x^2+6 x ) ( aligned & =3 ( 5 3 -1 )^2+6 [ ( 5 3 )-1 ] & =3 ( 5 3 +1-2 5 3 )+6 5 3 -6 & =5+3-6=2 aligned )

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