Determine the rule and give the next term in each of the following sequences.
1. 3, 12, 21, 30, 39, 48, …
2. 6, 12, 24, 48, 96, 192, …
3. 5, 10, 20, 35, 55, 80, …
4. 24, 12, 6, 3, 3
2
, …5. 4, 8, 24, 96, 480, …
6. 7, 16, 27, 40, 55, …
7. 4, 9, 16, 25, 36, 49, …
8. 1, 8, 27, 64, 125, 216, 343, …
9. 3, 6, 12, 21, 33, 48, …
10. 10, 100, 1,000, 10,000, …
Answers & Comments
Answer:
Number Patterns
12.1 Simple Number Patterns
A list of numbers which form a pattern is called a sequence. In this section, straightfor-
ward sequences are continued.
Worked Example 1
Write down the next three numbers in each sequence.
(a) 2, 4, 6, 8, 10, . . . (b) 3, 6, 9, 12, 15, . . .
Solution
(a) This sequence is a list of even numbers, so the next three numbers will be
12, 14, 16.
(b) This sequence is made up of the multiples of 3, so the next three numbers will be
18, 21, 24.
Worked Example 2
Find the next two numbers in each sequence.
(a) 6, 10, 14, 18, 22, . . . (b) 3, 8, 13, 18, 23, . . .
Solution
(a) For this sequence the difference between each term and the next term is 4.
Sequence 6, 10, 14, 18, 22, . . .
Difference 4 4 4 4
So 4 must be added to obtain the next term in the sequence. The next two terms are
22 4 26 + =
and 26 4 30 + = ,
giving 6, 10, 14, 18, 22, 26, 30, . . .
(b) For this sequence, the difference between each term and the next is 5.
Sequence 3, 8, 13, 18, 23, . . .
Difference 5 5 5 5
Adding 5 gives the next two terms as
23 5 28 + =
and 28 5 33 + = ,
giving 3, 8, 13, 18, 23, 28, 33, . . .
Sorry B0B0 KASI AKO EHH