Question

Find the sum of even numbers from 34 to 234 inclusive

Answer 1

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