1.3.2 Number Sequences Involving Fractions
A number sequence is a progression or an ordered list of numbers
governed by a pattern or rule.
In this section, we discuss:
- Arithmetic sequence involving fractions
- Geometric sequence involving fractions
1. Arithmetic Sequence
An arithmetic sequence is a sequence where the next term is obtained by
adding or subtracting a constant value from the current term.
Example 1.28
Find the next term in the sequence:
13,
12,
23,
…
Solution:
First, write the fractions using a common denominator of 6:
26,
36,
46
The pattern is adding
16
each time.
Next term =
46
+
16
=
56
2. Geometric Sequence
A geometric sequence is a sequence where each term is obtained by multiplying
or dividing the previous term by the same number, called the common ratio.
Example 1.29
Find the next term in the sequence:
12,
16,
118,
…
Solution:
Write the fractions using a common denominator of 18:
918,
318,
118
The pattern is dividing by 3 each time.
Next term =
118
÷ 3 =
154
Exercise 1.11
1. Fill in the next two terms in each of the following sequences.
(a)
13,
1,
1 23,
2 13, …
The sequence increases by 23 each time.
(b)
25,
15,
110,
120, …
Each term is obtained by dividing the previous term by 2.
(c)
1,
13,
19,
127, …
Each term is divided by 3 to get the next term.
(d)
110,
15,
310,
25, …
The sequence increases by 110 each time.
2. Create a number sequence of 5 terms starting with
32
and adding
12
to get the next number.
Start at 3/2 and keep adding 1/2 to get each next term.