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

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

Now, By using n^th term of an A.P. formula

t_n = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_n = n^th 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 n^th term of an A.P. we will find it’s sum

Where, n = no. of terms

a = first term

d = common difference

S_n = sum of n terms

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

Thus, S₁₇₄ = 30,450