Geometric sequences

There are 30 NRICH Mathematical resources connected to Geometric sequences
Summing geometric progressions
problem
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Summing geometric progressions

Age
14 to 18
Challenge level
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Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Double Trouble
problem
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Double trouble

Age
14 to 16
Challenge level
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Simple additions can lead to intriguing results...
Tiny Nines
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Tiny nines

Age
14 to 16
Challenge level
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What do you notice about these families of recurring decimals?
Sixty-Seven Squared
problem
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Sixty-seven squared

Age
16 to 18
Challenge level
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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?
Clickety Click and all the Sixes
problem
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Clickety click and all the sixes

Age
16 to 18
Challenge level
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What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
Magic Plant
problem
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Magic plant

Age
5 to 7
Challenge level
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On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

The Amazing Splitting Plant
problem
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The amazing splitting plant

Age
5 to 7
Challenge level
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Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Converging Product
problem
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Converging product

Age
16 to 18
Challenge level
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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)... ?
Circles ad infinitum
problem
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Circles ad infinitum

Age
16 to 18
Challenge level
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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?
Tower of Hanoi
problem
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Tower of Hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.