SL 1.2—Arithmetic sequences and series

The notation $a_n$ and $u_n$ are completely interchangeable. IB exams typically use $u_n$, so we'll stick with that — but don't be thrown if you see $a_n$ in other resources.

Consider the sequence: $3,7,11,15,19,\dots$

• First term: $u_1=3$
• Common difference: $d=7-3=4$
• Each term is found by adding 4 to the previous one.

Now try: $20,15,10,5,0,\dots$

• First term: $u_1=20$
• Common difference: $d=15-20=-5$ (negative $d$ means the sequence is decreasing)

To find $d$ quickly, subtract any term from the term that immediately follows it: $d=u_{n+1}-u_n$
Do this check with two different pairs — if $d$ is the same both times, you've confirmed it's arithmetic.