Download Sequences - Wey Valley School

The Wey Valley School & Sports
College
Mathematics Home Study
Page 1
PATTERNS
1. Consider this pattern of shapes:
UNIT: Algebra (Sequences)
Support work: Page 1
Core work: Page 2
Extension work: Page 3
(a) Draw the 5th shape
(b) Draw the 10th shape
2. Draw the next three shapes in each pattern:
(a)
(b)
In this unit you are required to look at a pattern and continue it
using logic or reasoning.
With number sequences the first step is to look at the difference
between the numbers. If the difference is the same each time,
this is called a constant difference or linear sequence. Each
number in a sequence is called a term; hence the first number in
a sequence is called the first term.
(c)
(d)
The rule for a sequence is called the “nth term”. For a linear
sequence the rule is always:
dn + (a – d)
where d = difference & a = first term.
3.
e.g. 4, 7, 10, 13, 16, …
d = 3 and a = 4 so the nth term = 3n + (4 – 3) = 3n + 1
So, if I wanted to know the 100th term in this sequence it would
be 3 × 100 + 1 = 301.
Page 2
(a) Draw the next picture in this sequence
(b) Count how many little squares are inside each shape
(c) What sort of number are these?
Page 3
NUMBER SEQUENCES
1. Write down the next three terms in each sequence:
(a) 14, 18, 22, 26, 30, …, …, …
(b) 3, 10, 17, 24, 31, …, …, …
(c) 17, 19, 21, 23, 25, …, …, …
(d) 31, 26, 21, 16, 11, …, …, …
(e) 53, 41, 29, 17, 5, …, …, …
2. What are the missing numbers in each of these sequences?
(a) …, 17, 15, 13, …
(b) 8, 11, …, 17, …
(c) 5, …, 27, 38, …
(d) 84, …, 76, 72, …
(e) 98, 109, …, 131, …
3. Write the next three multiples in each of the following
sequences:
(a) 4, 8, 12, 16, 20, …
(b) 13, 26, 39, 52, …
(c) 50, 100, 150, 200, …
(d) 7.2, 6.9, 6.6, 6.3, 6.0, …
(e) 10, 9½, 9, 8½, 8, …
(f) 4, 3¾, 3½, 3¼, 3, …
4. Write down the next four terms in each sequence (BE
CAREFUL!!!):
(a) 3, 4, 6, 9, 13, …
(b) 41, 40, 38, 35, 31, …
(c) 3, 4, 7, 11, 18, 29, …
(d) 1, 1, 2, 3, 5, 8, …
RULES & FORMULAE
1. (a) What sequence do you get when
1, 2, 3, 4, 5, … is put into this
number machine?
-2
(b) What number machine is
needed to get the outputs 10, 20, 30, 40, 50 from
inputting 1, 2, 3, 4, 5?
2. (i) Write down the first 6 terms of the sequences given by
these formulae:
(a) 2n (b) 6n (c) n + 7 (d) 10n – 1 (e) 4n + 3 (f) 3n – 2
(ii) What is the 10th term of each sequence?
3. Explain why the formula for the nth term of the sequence
9, 12, 15, 18, 21, …
is 3n + 6.
4. Find a formula for the nth term of these sequences:
(a) 8, 13, 18, 23, 28, …
(b) 16, 17, 18, 19, 20, …
(c) 11, 13, 15, 17, 19, …
(d) 6, 11, 16, 21, 26, …
(e) 80, 75, 70, 65, 60, …
5. (a) Write down the first 6 multiples of 12.
(b) Write the formula for the nth term of the sequence in (a).
(c) Write down the formula for the nth term of the sequence:
17, 29, 41, 53, 65, 77, …