Match Sequences

Don't play with real matches unless you are under the supervision of a responsible adult!

To play with virtual matches you need to save one of the bigger images on this page and then open it in Microsoft Paint.
You can then cut, paste, drag and drop the matches to your heart's content!

	How many matches are there in the puzzle?
	How many matches are there in this puzzle?
	How about this one?
Can you come up with a rule to help you find the number of matches in 50 triangles?

Think of it as a sequence of terms. Each term in the sequence contains more matches than the last one. Try to work out how each term is built or made from the last one. What is the difference between successive terms?

1st Term		3 matches
2nd Term		6 matches
3rd Term		9 matches
In this sequence the number of matches is equal to the term number X 3.	The fiftieth term would have 50x3 = 150 matches in 50 triangles.	In general (generalisation) the nth term ( n for number ) would contain n x 3 matches in n triangles.

	How many matches are there in this puzzle?
	How about this one?
	What about this one?
Can you come up with a rule to help you find the number of matches in 5,10 and 50 of these "bridge" shapes?

Think of it as a sequence of terms. Each term in the sequence contains 4 more matches than the last one. Try to work out how each term is built or made from the last one. What is the difference between successive terms?

1st Term		5 matches
2nd Term		9 matches
3rd Term		13 matches
This is how the third term is built
This is how the first term is built

In this sequence each term has 4 more matches than the last one.

The difference between terms is 4 matches.

The first term has one match plus the "difference" shape.

Thus the first term has 1 + 4 = 5 matches in it.

The second term has 1 + 4 + 4 = 1 + 2x4 = 9 matches

The third term has 1 + 4 + 4 +4= 1 + 3x4 = 13 matches

The nth term has 1 + n x 4 matches in it.

Try this out for n = 5 and check your answer with the picture below.

Important note!

Multiplication takes precedence over addition.
This means that you must x before you +.
If you want to + before you x then you must use brackets ( ).

Examples

1 + 2x3 = 7
(1+2)x3 = 3x3 = 9
2x3 + 4x5 = 6 + 20 = 26
(2+3)x(4+5) = 5x 9 = 45
2+3x4+5 = 2 + 12 + 5 = 19

What have we found out?

Sequence. A pattern of numbers or symbols arranged in a line or pattern. Term. One of the members of the sequence. Difference. How much bigger, smaller or whatever one term is compared to the next in the sequence. nth. 1st, 2nd, 3rd, 4th.....nth. Where n is any number that you are interested in!

Puzzle Move two matches to make 7 squares.