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Be Reasonable

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

Janusz Asked

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?

Prime AP

What can you say about the common difference of an AP where every term is prime?

Summats Clear

Age 16 to 18
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 $a > b$.