Sequences and Patterns: Practice Set 2
Sequences and Patterns: Practice Set 2 is a second practice round for 11+ sequences, revisiting term-to-term rules for linear sequences before pushing into finding the nth term, spotting non-linear patterns and using a sequence's rule to answer a reasoning question.
Method
- Find the term-to-term rule of a linear sequence by working out the constant difference between consecutive terms.
- To find the nth term of a linear sequence, use the constant difference as the coefficient of n, then compare it with the first term to find the number that must be added or subtracted.
- To find a term far along a sequence, substitute its position number into the nth term rule rather than counting on term by term.
- For a sequence that is not linear, such as one based on doubling, squares or a repeating pattern, look for a rule involving multiplication, powers or a repeating block instead of a constant difference.
- When a pattern is shown as a picture sequence, count how many extra shapes or dots are added at each step to find the term-to-term rule before writing an nth term expression.
- Check your nth term rule by substituting the first two position numbers back in and confirming they give the first two terms of the sequence.
Worked example
Find the nth term of the sequence 5, 9, 13, 17, 21, ...
- Find the constant difference between consecutive terms: 9 - 5 = 4, so the sequence goes up by 4 each time.
- Use this difference as the coefficient of n: the rule starts with 4n.
- Compare 4n to the first term when n = 1: 4 x 1 = 4, which is 1 less than the first term, 5, so 1 must be added.
- Write the full nth term rule: 4n + 1.
- Check the rule against the second term: 4 x 2 + 1 = 9, which matches, confirming the rule is correct.
Practice questions
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Q1Write the next two terms of the sequence 3, 8, 13, 18, ...Show answer
Answer: 23, 28
Q2Find the nth term of the sequence 2, 5, 8, 11, ...Show answer
Answer: 3n - 1
Q3Find the 10th term of the sequence with nth term 6n - 2.Show answer
Answer: 58
Q4A pattern sequence made from matchsticks has 4 matchsticks in pattern 1, 7 in pattern 2 and 10 in pattern 3. How many matchsticks will be in pattern 6?Show answer
Answer: 19 (the rule is 3n + 1, so 3 x 6 + 1 = 19)
Q5Find the nth term of the decreasing sequence 20, 17, 14, 11, ...Show answer
Answer: 23 - 3n
Q6A sequence is formed by doubling the previous term, starting at 3: 3, 6, 12, 24, ... Find the 6th term.Show answer
Answer: 96
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The nth term of a sequence is 5n + 3. Calculate the 12th term.
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A sequence begins 7, 12, 17, 22, ... (a) Find the nth term of the sequence. (b) Use your rule to determine whether 148 is a term in the sequence, showing your reasoning.
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A pattern sequence is made from tiles. Pattern 1 has 6 tiles, pattern 2 has 10 tiles and pattern 3 has 14 tiles. (a) Find the nth term for the number of tiles in pattern n. (b) Calculate how many tiles are needed for pattern 20.
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Free printable worksheet
Want more practice on paper? Download the sequences and patterns: practice set 2 worksheet pack - 15 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 11 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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