Find the sum of even numbers from 34 to 234 inclusive

We have

AP = 34,36,38 ...,234

a, (first term) = 34

n (total terms) = ?

d (common difference) = 2

so, a + (n-1) d = an

34 + (n-1) * 2 = 234

(n-1) 2 = 234-34

n-1 = 200/2

n = 100+1

n = 101

Now sum of the even no.

Sn = n/2 (2a+9n-1) d)

= 101/2 (2*34 + 100*2)

= 101/2 * 268

=101 * 134

= 13534