Question

What is the sum of all even integers between 99 and 301?

Answer 1

We know the first term must be: 100
Last term must be: 300
Number of terms = (300 - 100) / 2 + 1 = 200/2 + 1 = 100 + 1 = 101

Now use the arithmetic progression sum formula:
`S= (n)/(2)(a+l)`
where:
n = number of terms = 101
a = 1st term = 100
l = last term = 300

Therefore: S =
`(101)/(2)(100+300)= (101)/(2)*400=101*200=20200`