# Unit 13 Section 4 : Two-dimensional Number Patterns

This section looks at 2-dimensional number patterns. One of the most famous of these is Pascal's triangle.

## Pascal's Triangle

These are the first 4 rows of Pascal's triangle.
You can see that the first and last numbers in each row are always 1.
The other numbers are found by adding together the two numbers that are diagonally above them in the previous row.
For example, the left-hand "3" in the diagram above is found by adding together the 1 and the 2 in the row above.

Question: Work out the numbers which go in the next two rows , then click to see whether you are correct.

## Other Triangular Patterns

Look at the three triangles below:
You can see that every number in the first row of each diagram is a 1.
All the other numbers in the diagrams are found by adding the two numbers in the row above.

Question: Work out what the next two triangles will be, then use the buttons to see whether you are correct.

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to have another go. If you can't work out the right answer then click on to see the answer.

Question 1
In the first example above, you worked out the first 5 rows of Pascal's triangle.

Fill in the next three rows, using the check button to see whether each row is correct.
 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

Question 2
Look at the sequence of number triangles below:

Fill in the numbers in the next two diagrams in the sequence, checking each row as you go along.

Question 3
Look at the sequence of number triangles below:

Fill in the numbers in the next two diagrams in the sequence, checking each row as you go along.

Question 4
Look at the sequence of number triangles below:

Fill in the numbers in the next two diagrams in the sequence, checking each row as you go along.

Question 5
Look at the sequence of number triangles below:

Fill in the numbers in the next three diagrams in the sequence, checking each row as you go along.

Question 6
Below are the first 5 rows of a triangle of numbers.

Fill in the next three rows, using the check button to see whether each row is correct.
 2 2 2 2 4 2 2 6 6 2 2 8 12 8 2

Question 7
Look at the sequence of number triangles below:

(a) Fill in the numbers in the next diagram in the sequence, checking each row as you go along.
(b) What is the largest number in the 5th diagram in the sequence?
(c) What is the largest number in the 10th diagram in the sequence?
(d) What is the number of the diagram which has 384 as its largest number?

Question 8
Look at the sequence of number triangles below:

Fill in the numbers in the next two diagrams in the sequence, checking each row as you go along.

You have now completed Unit 13 Section 4
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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