Sequences

Maths, Physics Revision

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Look at this sequence
Sequence 1, 3, 5, 7, 9 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are twice the pattern number
less 1

So the nth number is 2n - 1

Look at this sequence
Sequence 3, 6, 9, 12, 15 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number

So the nth number is 3n

Look at this sequence
Sequence 5, 8, 11, 14, 17 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number
+2

So the nth number is 3n + 1

The rule for finding the nth number is to look
at the difference, use this to multiply
by n (e.g. 2n) then look what needs
to be added or subtracted to make it
fit the sequence
(e.g. 2n + 2) or (3n - 1)

In a square number sequence the nth number is n2
In a cube number sequence the nth number is n3
You can also add and subtract to square and cube
sequences
e.g. 2, 5, 10, 17 the nth number is n2 + 1
and 0, 3, 8, 15 would be n2 - 1

Try a test