MathsFreePrintable

Numerical Patterns Exploration

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Numerical Patterns Exploration

Find the rule for each sequence. Show your thinking where space is provided. For nth-term rules, the first number in a sequence is term 1.

Spot the Pattern

1.For the sequence 4, 9, 14, 19, 24, does each term get larger or smaller?

Increasing
Decreasing

2.For the sequence 31, 27, 23, 19, 15, is each term larger or smaller than the one before it?

Increasing
Decreasing

3.Find the constant difference in 8, 14, 20, 26, 32.

4.Find the constant difference in 42, 35, 28, 21, 14.

Continue and Describe Sequences

5.The sequence begins 6, 10, 14, 18. Complete the table with the values for terms 5 and 6.

Term number: 1 | 2 | 3 | 4 | 5 | 6

Term value: 6 | 10 | 14 | 18 | ____ | ____

6.For the sequence 6, 10, 14, 18, …, what is the 12th term?

7.Describe the rule for generating 11, 17, 23, 29, 35, … in words.

Write nth-Term Rules

8.Which rule gives the nth term of 5, 8, 11, 14, 17, …?

3n + 2
3n + 5
5n − 2
2n + 3

9.Write an nth-term rule for 7, 14, 21, 28, 35, …

10.Write an nth-term rule for 2, 6, 10, 14, 18, …

11.Write an nth-term rule for 38, 33, 28, 23, 18, …

12.Find the nth-term rule for 4, 10, 16, 22, 28, … Show how you used the first term and the constant difference.

Investigate and Match

13.Complete the missing terms in 9, ____, 19, 24, ____, 34.

14.Complete the missing terms in 64, 58, ____, 46, ____, 34.

15.Choose every statement that is true of an arithmetic sequence whose terms get larger.

Each term is greater than the term before it.
The constant difference is positive.
Each term is less than the term before it.
The constant difference is negative.
The terms increase by the same amount each time.

16.Match each sequence to its constant difference: (a) 6, 12, 18, 24, …; (b) 41, 35, 29, 23, …; (c) 3, 8, 13, 18, ….

(a) 6, 12, 18, 24, …
(b) 41, 35, 29, 23, …
(c) 3, 8, 13, 18, …

+5
+6
−6

Create and Apply

17.A sequence starts at 4 and increases by 8 each term. Write its first five terms.

18.A sequence starts at 4 and increases by 8 each term. Write an nth-term rule, where n = 1 gives the first term.

19.A fundraising group has $25 and saves another $15 each week. How much money will it have after 6 weeks, if it saves the first extra $15 after week 1?

20.A sequence has nth-term rule 5n + 3. What is the value of term 9?