Maths Teachers - help on number sequences please!

[reeldoop]

My ds is doing 11+ prep and there are lots of questions on number sequences where you have to extrapolate to another item further in the list. We can work them out manually, but i feel there must be a better way using some sort of formula but I am not sure how. They haven't done it in class.

For example this question:

Series of patterns with a number of tiles.

Pattern 1 = 1 tile
Pattern 2 = 4 tiles
Pattern 3 = 7 tiles
Pattern 4 = 10 tiles
Pattern 5 = 13 tiles

Question : How many tiles are there in pattern 7?
Answer: 19 (we just drew it out)

Question: Which number pattern has 70 tiles?
Answer: 24 (again, we tediously drew it out)

What is the better, formulaic way to approach these questions?

There is some sort of n + d type thing isn't there?

how would you advise a student to do these?

You need to work out the nth term.

If there is a constant gap of g between terms (eg g = 3 in the sequence above), then it will be of the form 3n+a (so 3n-2 in the one above)

If it's not a constant gap then you need to start looking at eg squared terms - so square numbers go 1, 4, 9, 16 - the gaps are 3, 5, 7 - so increasing by two each time - so gaps increasing by two each time tell you there's going to be an n^2 term in there.

why +a or -2 in this one?

My maths is rusty ..

Two ways of doing it

1. As it goes up in 3, compares the sequence to the 3 timetable of 3,6,9. The 3 timetable is 3n so to get from that to the sequence you are looking for you need to -2

1. A quicker way of doing it is by using this formula: nth term = the difference x n + 0th term

The “0th term” is just the term that goes before the first term if there is one.

If the sequence were 3, 6, 9, 12... then the nth term would just be 3n. (So for the first term, 3x1, for the second, 3x2 etc).

Because it isn't, we need to adjust by a constant. You want the first term to be 1, so that is 3x1 - 2. The second term is 3x2 - 2. The third is 3x3 - 2. Etc.

The BBC bitesize site has a helpful tutorial www.bbc.com/education/guides/z7j2pv4/revision/1

thankyou for that explanation! get it!

Following

Thanks to the BBC bitesize link.