Question

Find out sum of all even number in between 1 to 151​

Answer 1

This question can be solved by using concept of Arithmetic Progression ( AP ).

Now, the first even number between 1 to 150 = 2

So, a1 = 2

Last even number between 1 to 150 = 150

So an, = 150

Common difference ( d ) = second term - first term

= 4 - 2

= 2

We know that an = a+ ( n - 1 )

150 = 2+(n - 1 )× 2

150 - 2 = ( n - 1 ) × 2

148 = ( n - 1 ) × 2

148 / 2 = n - 1

74 = n - 1

74 + 1 = n

75 = n

We know that ,

sn = n upon 2 ( a + an )

= 75 upon 2 ( 2 + 150 )

= 75 upon 2 × 152

= 75 upon 2 × 152

75 × 76

= 5700

So, sum of all even number between 1 + 150 is 5700.