Christian Lawson-Perfect

Christian Lawson-Perfect on Find and use the formula for a geometric sequence 8 years, 5 months ago

Saved a checkpoint:

The gaps are all set as "mathematical expression", but there's no reason they shouldn't be "number entry" (apart from the formula part, obv.)

The parts of this question aren't coherent; you could keep the same sequence throughout, and ask the student to:

• Find the common ratio
• Give the formula for the $n$th term
• Calculate a given term.

Christian Lawson-Perfect on Finding the formula for the $n^{\text{th}}$ term of linear sequences 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Finding the formula for the $n^{\text{th}}$ term of linear sequences 8 years, 5 months ago

Saved a checkpoint:

I've split this into two parts - why make up your own part headers when Numbas can do it for you? It's important to let the student submit their answer to one part before moving on to another.

This question could very easily have steps - identify the first term, identify the common difference, and then you can write down the formula.

I've added a sentence to the top of the advice describing what needs to be done. A "plan of action" like this makes it easier to follow the more detailed parts of the solution.

I'd work this out by drawing up a table:

$n$	1	2	3
$a_n$	18	27	36
First differences		9	9

The formula is $a_n = a_1 + (n-1)d$. I can read off from the table that $a_1 = 18$ and $d = 9$.

There's a reason you're taught to do this stuff using tables at school - visually, you can see how $n$, $a_n$, and the common difference relate to each other as the sequence progresses. Without this, it can all seem like aimlessly shuffling numbers about.

Christian Lawson-Perfect commented on Finding the $n^{\text{th}}$ Term of a Quadratic Sequence 8 years, 5 months ago

Also, note that I used "first differences" and "second differences" - I thnk Lauren also spotted that it's tricky to keep track of all the differences floating about.

Christian Lawson-Perfect on Finding the $n^{\text{th}}$ Term of a Quadratic Sequence 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Finding the $n^{\text{th}}$ Term of a Quadratic Sequence 8 years, 5 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. 

For example,

$n$	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!

Christian Lawson-Perfect on Arithmetic sequences in an ice cream shop 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Arithmetic sequences in an ice cream shop 8 years, 5 months ago

Saved a checkpoint:

Part d should follow on from c, using the same sequence, and only ask for one (large) term. As it is, I've got to work out the formula for two new sequences and only get marked on the final answer.

Has something gone awry with the ice cream question? Jenny's friends both have tickets with larger numbers than hers. How does that help work out how many people got strawberry before Jenny? Unless you don't want to say explicitly how many flavours there are, that information is sort of a red herring.

Christian Lawson-Perfect on Finding unknown coefficients of a polynomial, using the remainder theorem 8 years, 5 months ago

Gave some feedback: Ready to use

Christian Lawson-Perfect on Finding unknown coefficients of a polynomial, using the remainder theorem 8 years, 5 months ago

Saved a checkpoint:

Good stuff!