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, …
(b) 25, 15, 110, 120, …
(c) 1, 13, 19, 127, …
(d) 110, 15, 310, 25, …
2. Create a number sequence of 5 terms starting with 32 and adding 12 to get the next number.