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Question

Find the sum of even positive integers between 1 and 200.

Solution
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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)=(42)=2

Last term, L=198

We know,

L=a+(n1)d

198=2+(n1)2

198=2+2n2

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

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