Question

find the sum 2+4+6+....+200

Answer 1

This series will form an A.P.

Where,

First term ( a ) = 2

Last term ( l ) = 200

Common Difference = 2nd term - 1st term = 4 - 2 = 2.

Let number of terms are ' N'.

Last term = First term + ( No. of terms - 1 ) Common difference


200 = 2 + ( N - 1 ) 2

200 = 2 + 2 N - 2

2 N = 200

 N = 200 / 2 = 100.

Sum of ' N ' terms = No. of terms / 2 ( First term + Last term )

                             = ( 100 / 2 ) ( 2 + 200 )

                             = 50 ( 202 )

                             = 10,100.

So, 2 + 4 + 6 + ......... + 200 = 10,100.