Find the sum of even positive integers between 1 and 200.
Let , The sum of even positive integers between 1 and 200 be S(n)
The given are the even numbers between 1 and 200 in the form of AP :
2,4,6.......198
Here,
First term, a=2
Common Difference, d=a(2)−a(1)=(4−2)=2
Last term, L=198
We know,
L=a+(n−1)d
198=2+(n−1)2
198=2+2n−2
198=2n
n=1982
n=99
We know,
S(n)=n2(a+L)
S(99)=992(2+198)
=99×100
=9900
Thus, the sum of even positive integers between 1 and 200 is 9900