Sir\Madam please explain me this question on Arithmetic Progressions!

Asked by  | 17th Jan, 2010, 07:29: PM

Expert Answer:

let the first term and common diff be a and d respectively.

let the number of terms be odd, say, 2n+1

then the n+1 th term is the middle term.=a+[(n+1)-1]=a+n

so we have to show that

 sum of all the 2n+1 terms =the n+1th term (2n+1)

LHS=[(2n+1)/2][a+{a+2n}]....using the formula for sum of n terms of an A.P.


=number of terms (the middle term)

Answered by  | 17th Jan, 2010, 10:30: PM

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