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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?
Summats Clear
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.
Stage: 5 Challenge Level: 
In the video below, Alison works out \(\sum_{i=1}^{10} i\).
How could you adapt her method to work out the following sums?
- $\sum_{i=1}^{100} i$
- $2+4+6+\dots+96+98+100$
- $\sum_{k=1}^{20} (4k+12)$
- $37+42+47+52+\dots+102+107+112$
- The sum of the first $n$ terms of the sequence $a, (a+d), (a + 2d), (a + 3d) \dots$
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?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.