Search by Topic

Resources tagged with Geometric sequence similar to Seriesly:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 18 results

Broad Topics > Sequences, Functions and Graphs > Geometric sequence

problem icon

Sum the Series

Stage: 5

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.

problem icon

Converging Product

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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)... ?

problem icon

Weekly Challenge 35: Clickety Click and All the Sixes

Stage: 5 Short Challenge Level: Challenge Level:1

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

problem icon

Binary Squares

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Clickety Click and All the Sixes

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Proof Sorter - Geometric Series

Stage: 5 Challenge Level: Challenge Level:1

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

problem icon

Sixty-seven Squared

Stage: 5 Challenge Level: Challenge Level:1

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?

problem icon

Summing Geometric Progressions

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

problem icon

Squaring the Circle and Circling the Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Geometric Parabola

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Generally Geometric

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Cellular

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Cellular is an animation that helps you make geometric sequences composed of square cells.

problem icon

Golden Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Ruler

Stage: 5 Challenge Level: Challenge Level:1

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?

problem icon

Circles Ad Infinitum

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Sierpinski Triangle

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Von Koch Curve

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.