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Christian Lawson-Perfect 2 years, 9 months ago
Saved a checkpoint:
The layout of the advice is very hard to follow.
I would work this out by drawing up a table with rows for $n$, $a_n$, and first and second differences.
$n$ 1 2 3 4 $a_n$ 15 22 33 48 First differences 7 11 15 Second differences 4 4
Because the second difference is $4$, I know that the coefficient of $x^2$ is $4/2 = 2$.
Then I can add a row for $a_n - 2n^2 = bn+c$:
$n$ 1 2 3 4 $a_n$ 15 22 33 48 $2n^2$ 2 8 18 32 $a_n-2n^2$ 13 14 15 16
So $bn+c = n+12$, and the formula for the whole sequence is $a_n = 2n^2+n+12$.
Sometimes, a good layout can save a lot of verbiage!
Lauren Richards 2 years, 9 months ago
- So after you have found the difference between the sequential terms, and then found the difference between the differences, which you found in the question I did to be 8, it is not clear how you would decide to start the nth term off as 8/2n^2. I think you need to add in a line explaining your reasoning for this.
- I don't think the first sentence reads very well. Maybe something more like "We first need to calculate the differences between the terms in the sequence.". and then for the second bit of writing "We can then calculate the differences of the term differences." I totally get that that is quite hard to word without being confusing.
- I think "original sequence" should probably be capitalised.
- In the advice, the second bit of writing that finishes with the word differences, is missing a full stop. You're also missing a comma at the end of "difference" near the end of the advice but I think this sentence should be re-worded anyway as it starts with "If", but then doesn't really end it like you would expect. I think it should be something like "We should first find the common difference.".
- No fault of yours but it gets a little confusing with the amount of differences being mentioned, and I think when you refer to the "sequence of differences" you should have sequence of differences in brackets when you first make it to make it clear when you next refer to it.
- I think differences sequence should be capitalised.
- At the end, you're calculating the difference between 2n and the sequence of differences but you haven't done that in the same way as you have done earlier in the question advice and I think you probably should do.
- One time I did the question, it said "Then we can find the difference between 1n and our sequence of differences" so I think you should make sure it just states "n" in this case.
- I think this is a good question, and tricky to make clear!
Vicky Hall 2 years, 9 months ago
I would reword the question to say 'Find the formula for the $n$th term of the quadratic sequence'.
The advice is good but think the last part, where you find the constant, would look better if it were laid out like the previous part, so you show the student what the sequence $3n^2+3n$ looks like compared to the original sequence. You also need to remove the reference to part b).
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