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Transcript
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Maths for ages 11-16
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Ltd 2009
Naming sequences
Here are the names of some sequences which you may
2, 4, 6, 8, 10, ...
Even numbers (or multiples of 2)
1, 3, 5, 7, 9, ...
Odd numbers
3, 6, 9, 12, 15, ...
Multiples of 3
5, 10, 15, 20, 25, ... Multiples of 5
1, 4, 9, 16, 25, ...
Square numbers
1, 3, 6, 10, 15, ...
Triangular numbers
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Sequences from real life
Number sequences are all
around us.
Some sequences, like the
ones we have looked at today
complex rules, for example, the
time the sun sets each day.
Some sequences are completely random, like the sequence of
numbers drawn in the lottery.
What other number sequences can
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Sequences that increase in equal steps
We can describe sequences by finding a rule that tells us
how the sequence continues.
To work out a rule it is often helpful to find the difference
between consecutive terms.
For example, look at the difference between each term in
this sequence:
3,
7,
+4
11,
+4
15,
+4
19,
+4
+4
23,
+4
27,
31, ...
+4
This sequence starts with 3 and increases by 4 each time.
Every term in this sequence is one less than a multiple of 4.
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Sequences that increase by multiplying
Some sequences increase or decrease by multiplying or
dividing each term by a constant factor.
For example, look at this sequence:
2,
4,
×2
8,
×2
16,
×2
32,
×2
64,
×2
128, 256, ...
×2
×2
This sequence starts with 2 and increases by multiplying
the previous term by 2.
All of the terms in this sequence are powers of 2.
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Fibonacci
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Finding missing terms
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Name that sequence!
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