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2015-05-09T10:57:11+05:30

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1st Method:
Sn (Sum of the 'n' numbers) = n/2 (2a+(n-1)d)

there given last no. is 250, so the no.of even numbers here is 250/2 i.e., 125
i.e., n=125, a (1st number) = 2, l (last number)  =  250
then,
Sn = n/2 (a+l)
     = 125/2 (2+250)
     = 125×252/2
     = 125(126)
     = 15750
therefore, the sum of all the even no.s upto 250 is 15750

2nd Method:
Sn = n/2 (2a+(n-1)d)
we got n= 250/2 = 125, a=2, d (common difference) = 2
Sn = 125/2 (2(2)+(125-1)2)
      = 125(4+248)/2
      = 125(252)/2
      = 125(126)
      = 15750
hence, 
the sum of all the even no.s upto 250 is 15750
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2015-05-09T11:00:36+05:30

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This is an ap with common diff.. 2 
 so use formula n(a1+an)/2

on this ap there will be 125 terms
 
so ..n=125
therefore 
  Sn=125(2+250)/2
      =(125*252)/2
      =15750
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nth term = first term + (number of terms - 1)*common difference /2
applying it in the above example , nth term = 250 , first term = 2 and common difference = 2 , substitute these values and you will find the number of terms in Arithmetic Progression ..
and Finally calculate the sum of series = (first term + last term )*number of terms / 2 !!!
enjoy !!