Mathematics

An arithmetic progression is completely determined by just two unknowns: the first term $a$ and common difference $d$. You have two pieces of information—the sum of 20 terms and the value of the 20th term—which gives you exactly two equations. The key is to write each constraint using the standard formulas ($S_n = \frac{n}{2}(2a + (n-1)d)$ and $a_n = a + (n-1)d$), then solve the resulting system algebraically.

An arithmetic progression is completely determined by just two unknowns: the first term $a$ and common difference $d$. You have two pieces of information—the sum of 20 terms and the value of the 20th term—which gives you exactly two equations. The key is to write each constraint using the standard formulas ($S_n = \frac{n}{2}(2a + (n-1)d)$ and $a_n = a + (n-1)d$), then solve the resulting system algebraically.