### 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?

### Prime AP

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

# Summats Clear

##### Stage: 5 Challenge Level:

Investigate special cases for small $n$ first.

Can you spot patterns in the sums for $n=3$, $4$, $5$, $6$, $7 \dots$?