Download 8.1_Sequences

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, …
Term-to-term rule (recurrence
relation – give first term in sequence and the
relationship between successive terms)
General term / nth term
u1 = first term
 u2 = second 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
 2,4,6,8,...
Do the signs of the terms alternate?
Ignore the signs – Find the nth term.
2n(-1)n
(-1)n = -1 when n is odd
(-1)n = +1 when n is even
(1)
n 1
(1)
n 1
10,12,14,16,...
(2n  8)(1)
n 1
9,7,5,3,...
(2n  11)(1)
n 1
1,8,27,64,81,...
n (1)
3
n 1
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.
1,4,9,16,25,...
n (1)
2
n 1
1,2,4,8,...
Look for powers of numbers
2
n 1
th
n
term is given:
1. Find the first 4 terms
of the sequence.
1
xn  n
2
2. Which term in the
sequence is
1
1024
3. Express the
sequence as a
recurrence relation
A sequence is defined by a recurrence relation of
the form
M  aM  b
n 1
n
Given that M1 = 10, M2 = 20, M3 = 24, find the value
of a and the value of b and hence find M4.
Page 133 Exercise 8A
Questions 1 a, c, e
2 a, b, c and 6