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?
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
In the video below, Alison works out \(\sum_{i=1}^{10} i\).
How could you adapt her method to work out the following sums?
After how many terms would $17+21+25+\dots$ be greater than $1000$?
Can you find the sum of all the integers less than $1000$ which are not divisible by $2$ or $3$?
Can you find a set of consecutive positive integers whose sum is 32?