Question

The sum of all even numbers upto 100 is---------?

Answer 1

The even numbers have a common difference of 2. Your first term is 2 (I'm assuming you want to sum from numbers greater than or equal to 1 up to 100).

From the formula for the nth term in an arithmetic sequence, we have,

a[n] = a[1]+(n-1)d, and so,
100 = 2 + (n-1)*2 which yields n =50 - that is, you'll have 50 terms to sum.

The sum of the first 50 terms is then given by,

S[n] = (n/2)(a[1]+a[n])
= (50/2)(2+100)
= 2550

Answer 2

Thank you

Answer 3

No worries.