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Martin Kilian 6 months, 1 week ago
Gave some feedback: Ready to use
Luis Hernandez 10 months, 3 weeks ago
Gave some feedback: Has some problems
Luis Hernandez 10 months, 3 weeks ago
Gave some feedback: Ready to use
Christian LawsonPerfect 2 years, 3 months ago
Saved a checkpoint:
I don't think this question is worth saving. I've split part d, about finding a given term, into a separate question.
Ideally, there'd be a question combining parts a and b, asking you to sort a few sequences into linear, quadratic, geometric, or other.
I don't think there's any point in the parts which ask you to give the next three terms of the triangle, square, and cube numbers.
Christian LawsonPerfect 2 years, 3 months ago
Gave some feedback: Should not be used
Elliott Fletcher 2 years, 4 months ago
Published this.Bradley Bush 2 years, 4 months ago
Gave some feedback: Needs to be tested
Bradley Bush 2 years, 4 months ago
Thank you for the feedback Christian:
 I have added tables to the feedback for parts a and b to make the working easier to follow.
 I have added a table to the feedback for c also to analyse the difference between terms but I have included Hannahs solution using the formula as an alternative method of solving this.
 I have altered question d to be the more generic randomisable sequence equation which you suggested.
 I attempted to explain the solution using a table here to find the differences too but I am not too sure how thoroughly this would explain the way you work out that the sequence is squared numbers and cubic numbers without simply recognising them. Nor am I confident I even know how to recommend solving this problem if you do not recognise the squared or cubic terms on your own?
Christian LawsonPerfect 2 years, 4 months ago
Gave some feedback: Has some problems
Christian LawsonPerfect 2 years, 4 months ago
Saved a checkpoint:
Advice for part a could show each sequence with the common differences underneath, so it's easy to see which are linear. That's how I'd work it out.
Similarly with common ratios for part b.
For part c, I just use the fact that the difference between consecutive triangle numbers increases by 1 at each step. A drawing of the first few triangle numbers would help show this. While you can use the formula, it's not obvious, and you'd look at common differences first.
In part d, rather than using the triangle sequence in particular, I'd give a formula of the form $\frac{an(n+b)}{c}$ (what constraints are there on randomising this?)  you want to see that the student's comfortable with using a formula to get the nth term of a sequence without working out all the previous terms.
Part e relies on noticing that the sequences are the squares and cubes, respectively. How would you work this out? It's not enough to just state it in the advice. You might look at common differences, then make a guess that it's $n^2$ or $n^3$. The advice should show this experimental thinking  is it really $n^2$? How do we check? Draw a table of $n$ against $a_n$?
Hannah Aldous 2 years, 4 months ago
Gave some feedback: Needs to be tested
Hannah Aldous 2 years, 4 months ago
Created this as a copy of Finding the $n^{\text{th}}$ Term of a Quadratic Sequence.No variables have been defined in this question.
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