Sequences and Recursive Rules Notes
Y12 Applications
Recursive rules otherwise known as recursive formula
1.
•
are rules which tell us how a sequence of numbers _________________.
•
tell us how to find the __________________in the sequence.
•
must also include the ___________________, so that the same numbers are always generated.
For the sequence
4, 7, 10, 13, 16…
a) If T1 = 4, how do you find T2 ?
b) Does the pattern continue?
c) If the first term is Tn, how do you find the next term Tn+1 ?
d) Write a recursive rule so that this exact sequence can be generated by this rule.
2.
For the sequence
100, 50, 25, 12.5, 6.25…
a) If Tn = 25, how do you find Tn+1 ?
b) If Tn = 25, what is the value of Tn–1 ?
c) Complete the following recursive rules for this sequence
3.
(i)
Tn+1 =
(ii)
Tn
(iii)
Tn–1 =
=
Determine the first four terms in the following sequences.
a) Tn+1 = 2 Tn + 4
T1 = 1
b) Tn
T1 = 20
= 0.5 Tn–1
c) Tn+2 = 10 Tn+1 – 10
T1 = 2
d) Tn+1 = 5 Tn
T3 = 50
e) Tn
T2 = 16
f)
= 3 Tn–1 + 1
Tn+2 = Tn+1 + Tn
T1 = 2, T2 = 4
g) Tn+2 = Tn+1 – Tn
T1 = 2, T2 = 4
h) Tn
T1 = 2, T2 = 4
= Tn–1 – Tn–2
4.
Determine a recursive rule for the following sequences.
a) 3, 7, 11, 15…
b) 3, 7, 15, 31…
c) 160, 40, 10, 2.5…
d) 5, 5, 10, 15, 25, 40…
e)
f)
g) The sequence generated by the equation, y = 2x + 4.
h) The sequence generated by the equation, y = 2x.
5.
An arithmetic sequence involves addition or subtraction to obtain the next term.
Which sequences in question 4 are arithmetic?
Write “arithmetic” next to each of them.
6.
A geometric sequence involves multiplication to obtain the next term.
Which sequences in question 4 are geometric?
Write “geometric” next to each of them.
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