Q. 34.1( 43 Votes )

Find the sum of all even numbers from 1 to 350.

Answer :

List of even natural number between 1 to 350 is

2,4,6,…….348


Where first term a = 2


Second term t1 = 4


Third term t2 = 6


Thus, common difference d = t2 – t1 = 6 – 4 = 2


tn = 348 (As we have to find the sum of even numbers between 1 and 350 therefore excluding 350 )


Now, By using nth term of an A.P. formula


tn = a + (n – 1)d


where n = no. of terms


a = first term


d = common difference


tn = nth terms


we can find value of “n” by substituting all the value in formula we get,


348 = 2 + (n – 1) × 2


348 – 2 = 2(n – 1)


346 = 2(n – 1)



n = 173 + 1 = 174


Now, By using sum of nth term of an A.P. we will find it’s sum



Where, n = no. of terms


a = first term


d = common difference


Sn = sum of n terms


Thus, Substituting given value in formula we can find the value of Sn






Thus, S174 = 30,450

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