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Question

The sum up to n terms of an AP in which the first term is a, last term is l, and the common difference is d, is ___
  1. n2(2a+(n1)d)
     
  2. n2(a+l)
     
  3. n2(a+(n1)d)
     
  4. n2(2a+l)


Solution

The correct options are
A n2(2a+(n1)d)
 
B n2(a+l)
 
We know that sum upto n terms of an AP with first term a and common difference d is
n2(2a+(n1)d)
=n2(a+a+(n1)d)----- (1)
We know that a+(n1)d is the  nth term, which is the last term.
Substituting the value of last term i.e. a+(n1)d equals to l in formulae (1).
Hence, Sn=n2(a+l)

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