How do you find (and simplify) an expression, in terms of n, for the sum of the first n terms of the series 5 + 8 + 11 + 14 + ... ?

Normally, this would be quite hard! We'd have to play around with the sequence and try different formulas until something worked. Luckily, this is what we call an "Arithmetic Series". That's because when we go from one term to the next, it's always the same difference between the two numbers. In this case, it's three. We know a formula for this!

The formula for the sum of the first n terms of an arithmetic series is given by Sn = n(a1 + an)/2. We use a1 to mean the very first term of the series, and an to mean the nth term of the series. If in our example we had to find the sum of the first five terms, we'd do Sn = 5(5 + 17)/2 = 55.