What do all the odd numbers lying between 20 and 80 add up to?

The odd numbers are 21, 23, ..., 79, so $n=\frac{79-21}{2}+1=30.S=\frac{30}{2}$$(21+79)=15(100)=1500$. The value 1450 uses $n=29$ and 1550 uses $n=31$ — both miscount the terms. 3000 drops the factor $\frac{1}{2}$. The shortcut "sum of the first $n$ odd numbers = $n^2$" does not apply here, because this list does not start at 1.