Mathematics

An arithmetic progression has a constant difference between consecutive terms, so once you know any two terms, you can find that common difference $d$ and the first term $a$. The key insight is to use the two given terms to set up a system of equations: since $a_n = a + (n-1)d$, you have two unknowns ($a$ and $d$) and two equations. Solve for $d$ first—it's the simplest path—then use it to find the 30th term.

An arithmetic progression has a constant difference between consecutive terms, so once you know any two terms, you can find that common difference $d$ and the first term $a$. The key insight is to use the two given terms to set up a system of equations: since $a_n = a + (n-1)d$, you have two unknowns ($a$ and $d$) and two equations. Solve for $d$ first—it's the simplest path—then use it to find the 30th term.