### Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

### Proof Sorter - Sum of an AP

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

# Summats Clear

##### Stage: 5 Challenge Level:

Find the sum, $f(n)$, of the first $n$ terms of the sequence: \begin{equation*} 0, 1, 1, 2, 2, 3, 3, \dots , p, p, p +1, p + 1, \dots \end{equation*}

Go on to prove that $f(a + b) - f(a - b) = ab$, where $a$ and $b$ are positive integers and $a > b$.