CBSE Class 11-science Answered
Sir\Madam please explain me this question on Arithmetic Progressions!
Asked by | 17 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.
=(2n+1)(a+n)
=number of terms (the middle term)
Answered by | 17 Jan, 2010, 10:30: PM
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