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: $S= \frac{n}{2}(a+l)$
where:
n = number of terms = 101
a = 1st term = 100
l = last term = 300

Therefore: S = $\frac{101}{2}(100+300)= \frac{101}{2}*400=101*200=20200$