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Sequences and series:
Arithmetic series
8.1 Sequences
LO: To be able to find the formula for the terms of a sequence
8, 11, 14, 17, …
u1 = first term
u2 = second term…
Term-to-term rule (recurrence
relation – give first term in sequence and the
relationship between successive terms)
General term / nth term
5, 9, 13, 17, ….
Term-to-term rule
(recurrence relation)
General term / nth term
15, 12, 9, 6, ….
Term-to-term rule
(recurrence relation)
General term / nth term
Ignore the signs – Find the nth term.
(-1)n = -1 when n is odd
(-1)n = +1 when n is even
Do the signs of the terms alternate?
2n(-1)n
1)1( n
,...8,6,4,2
1)1( n
1)1)(82( nn
,...16,14,12,10
1)1)(112( nn
,...3,5,7,9
If the numbers go up rapidly and are not
obviously being multiplied by the same
number, the nth term could contain a
square or a cube or a quadratic.
,...81,64,27,8,1
13 )1( nn
,...25,16,9,4,1
12 )1( nn
,...8,4,2,1
12 n
Look for powers of numbers
nth term is given:
1. Find the first 4 terms
of the sequence.
nnx2
1
2. Which term in the
sequence is
3. Express the
sequence as a
recurrence relation
1024
1
A sequence is defined by a recurrence relation of
the form
Given that M1 = 10, M2 = 20, M3 = 24, find the value
of a and the value of b and hence find M4.
baMM nn 1
Page 133 Exercise 8A
Questions 1 a, c, e
2 a, b, c and 6