Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
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?
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
Investigate special cases for small $n$ first.
Can you spot patterns in the sums for $n=3$, $4$, $5$, $6$, $7 \dots$?