What is the total of all even numbers lying strictly between 100 and 200?

The evens are 102, 104, ..., 198, so $n=\frac{198-102}{2}+1=49.S=\frac{49}{2}$$(102+198)=49(150)=7350$. The value 7200 uses $n=48$, forgetting the "+1" when counting terms. 7650 wrongly includes both 100 and 200, giving 51 terms. 14700 omits the factor $\frac{1}{2}$.