The third term of an arithmetic progression is 11 and the seventh term is 27. Find the twentieth term.

With first term $a$ and common difference $d$: $a + 2d = 11$ and $a + 6d = 27$. Subtracting gives $4d = 16$, so $d = 4$ and $a = 3$. The twentieth term is $a + 19d = 3 + 76 = 79$. Using $20d$ instead of $19d$ gives 83.