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#### Resources tagged with Geometric sequences similar to Harmonically:

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### There are 20 results

Broad Topics > Patterns, Sequences and Structure > Geometric sequences

### 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.

### Vanishing Point

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

How can visual patterns be used to prove sums of 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?

### 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?

### 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?

### 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)?

### 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?

### 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.

### Tiny Nines

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

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

### 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!

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

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

### 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?

### 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.

### 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.

### 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?