# Resources tagged with: Geometric sequences

Filter by: Content type:
Age range:
Challenge level:

### There are 20 results

Broad Topics > Patterns, Sequences and Structure > Geometric sequences

### Golden Fibs

##### Age 16 to 18 Challenge Level:

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

### Converging Product

##### Age 16 to 18 Challenge Level:

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

### Binary Squares

##### Age 16 to 18 Challenge Level:

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

### Clickety Click and All the Sixes

##### Age 16 to 18 Challenge Level:

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

### Sum the Series

##### Age 16 to 18

This article by Alex Goodwin, age 18 of Madras College, St Andrews describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n terms.

### Clickety Click

##### Age 16 to 18 Short Challenge Level:

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

### Vanishing Point

##### Age 14 to 18 Challenge Level:

How can visual patterns be used to prove sums of series?

### Proof Sorter - Geometric Series

##### Age 16 to 18 Challenge Level:

Can you correctly order the steps in the proof of the formula for the sum of a geometric series?

### Sixty-seven Squared

##### Age 16 to 18 Challenge Level:

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

### Ruler

##### Age 16 to 18 Challenge Level:

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?

### Generally Geometric

##### Age 16 to 18 Challenge Level:

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

### Summing Geometric Progressions

##### Age 14 to 18 Challenge Level:

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

### Squaring the Circle and Circling the Square

##### Age 14 to 16 Challenge Level:

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

### Production Equation

##### Age 16 to 18 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

### Sierpinski Triangle

##### Age 16 to 18 Challenge Level:

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

### Von Koch Curve

##### Age 16 to 18 Challenge Level:

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

### Geometric Parabola

##### Age 14 to 16 Challenge Level:

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.