To find the sum of the even numbers we can calculate directly by writing the them and adding , but if the range is big then it would take a lot of time to find their sum . In this case we have a formula to calculate the sum of the series that is Sum= xn(n+1)/2
And another is Sum= n(a+d)/2 where a is the last term and d is the first term.
We can use the first formula where the n is and x is the common difference between any two terms the number of terms, that is xn(n+1)/2
,we can calculate the number of even terms between 1 and 31.See the number of terms between 1 and 30 is 30-1 = 30 terms and to calculate the number of even terms we will divide 30 by 2 which is 15 and the difference between any two even number is 2 , So x=2
So keeping 15 in place of n and 2 in x in the formula xn(n+1)/2
we will get
Hence, the sum of the even terms between 1 and 31 is 240.
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