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

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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