# Resources tagged with: Iteration

### There are 13 results

Broad Topics >

Patterns, Sequences and Structure > Iteration

##### Age 14 to 16

Challenge Level

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$
for different choices of the first two terms. Make a conjecture
about the behaviour of these sequences. Can you prove your
conjecture?

##### Age 14 to 16

Challenge Level

Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .

##### Age 14 to 18

Challenge Level

Investigate the sequences obtained by starting with any positive 2
digit number (10a+b) and repeatedly using the rule 10a+b maps to
10b-a to get the next number in the sequence.

##### Age 14 to 16

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

##### Age 14 to 16

Challenge Level

It's like 'Peaches Today, Peaches Tomorrow' but interestingly
generalized.

##### Age 14 to 16

Challenge Level

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

##### Age 14 to 18

Challenge Level

Take three whole numbers. The differences between them give you
three new numbers. Find the differences between the new numbers and
keep repeating this. What happens?

##### Age 14 to 16

Challenge Level

Keep constructing triangles in the incircle of the previous triangle. What happens?

##### Age 14 to 16

Challenge Level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

##### Age 11 to 14

Challenge Level

Choose any 4 whole numbers and take the difference between
consecutive numbers, ending with the difference between the first
and the last numbers. What happens when you repeat this process
over and. . . .

##### Age 14 to 16

Challenge Level

Explore the transformations and comment on what you find.

##### Age 11 to 18

Challenge Level

What happens when a procedure calls itself?

##### Age 7 to 16

Challenge Level

A Short introduction to using Logo. This is the first in a twelve part series.