Question

find the sum of even positive integers between 1 and 200

Answer 1

Hope this helps...
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Answer 2

Hey mate..
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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 :--

AP:- 2, 4, 6 .......198 ( °•° Between 1 and 200 )

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

=> 198 / 2 = n

=> 99 = n

We know,

S(n) = n/2 ( a + L )

•°• S (99) = 99/2 ( 2 + 198 )

= 99 × 100

= 9900

Thus, the sum of even positive integers between 1 and 200 is 9900

Hope it helps !!