Mickey Being Brilliant

Since the difference between the second day and the first day is 5, the third day and the second is 5, ... and so on, we have an arithmetic progression with a common difference of 5. Let $x$ be the number of problems he did on the first day, then the terms are

$x,x+5,x+10,x+15,x+20$

We can use the formula $s=\dfrac{n}{2}(a_1+a_2)$ . So we have

$100=\dfrac{5}{2}(x+x+20)$

$200=5(2x+20)$

$40=2x+20$

$x=10$

Finally, the third term is

$x+10=10+10=$ $\boxed{20}$