UK K12 GCSE/A-Level: Year 6 KS2 Mathematics - Algebra, Simple Formulae and Sequences

Learning objectives

By the end of this topic, students will be able to:

• Understand the concept of a simple formula and its application in real-life scenarios.
• Recognize and create sequences using addition or subtraction.
• Use algebraic notation to represent unknown values in sequences.
• Solve simple problems involving sequences and formulas.
• Apply mathematical reasoning to solve problems involving sequences and formulas.

Core concepts

A formula is a way of expressing a relationship between variables using mathematical symbols. In the context of sequences, a formula can be used to describe the pattern of numbers in the sequence. For example, the formula for the sequence 2, 5, 8, 11, ... is given by:

n² + 1

where n is the term number.

A sequence is a list of numbers in a particular order. Sequences can be created using various methods, such as addition or subtraction. For example, the sequence 2, 4, 6, 8, ... is created by adding 2 to each previous term.

Algebraic notation is used to represent unknown values in sequences. For example, the sequence 2, 4, 6, 8, ... can be represented as:

2, 2 + 2, 2 + 4, 2 + 6, ...

where the unknown value is represented by the variable '2'.

Worked examples

Example 1

Find the next term in the sequence 2, 5, 8, 11, ...

Using the formula n² + 1, we can substitute n = 4 to find the next term:

4² + 1 = 16 + 1 = 17

Therefore, the next term in the sequence is 17.

Example 2

Create a sequence using the formula 3n + 2, where n is the term number. Find the first five terms of the sequence.

Substituting n = 1, 2, 3, 4, 5 into the formula, we get:

3(1) + 2 = 5 3(2) + 2 = 8 3(3) + 2 = 11 3(4) + 2 = 14 3(5) + 2 = 17

Therefore, the first five terms of the sequence are 5, 8, 11, 14, 17.

Common misconceptions

• Students may confuse the concept of a formula with a sequence.
• Students may struggle to apply algebraic notation to represent unknown values in sequences.
• Students may incorrectly use the formula for a sequence, resulting in an incorrect answer.

Exam tips

• Make sure to read the question carefully and understand what is being asked.
• Use algebraic notation to represent unknown values in sequences.
• Apply mathematical reasoning to solve problems involving sequences and formulas.
• Check your answer to ensure it is reasonable and makes sense in the context of the problem.

MCQs with explanations

MCQ 1 [F]

What is the next term in the sequence 2, 5, 8, 11, ...?

A) 14 B) 17 C) 20 D) 22

Correct answer: B) 17 Why the distractors fail: - A) 14 is an incorrect answer because it does not follow the pattern of the sequence. - C) 20 is an incorrect answer because it is not a multiple of 3. - D) 22 is an incorrect answer because it is not a multiple of 3.

MCQ 2 [H]

Create a sequence using the formula 2n + 1, where n is the term number. Find the first three terms of the sequence.

A) 3, 5, 7 B) 5, 7, 9 C) 2, 4, 6 D) 1, 3, 5

Correct answer: A) 3, 5, 7 Why the distractors fail: - B) 5, 7, 9 is an incorrect answer because it does not follow the pattern of the sequence. - C) 2, 4, 6 is an incorrect answer because it does not follow the pattern of the sequence. - D) 1, 3, 5 is an incorrect answer because it does not follow the pattern of the sequence.

MCQ 3 [F]

What is the formula for the sequence 2, 4, 6, 8, ...?

A) n² + 1 B) 2n C) n + 2 D) n - 2

Correct answer: C) n + 2 Why the distractors fail: - A) n² + 1 is an incorrect answer because it does not follow the pattern of the sequence. - B) 2n is an incorrect answer because it does not follow the pattern of the sequence. - D) n - 2 is an incorrect answer because it does not follow the pattern of the sequence.

MCQ 4 [H]

Find the next term in the sequence 3, 6, 9, 12, ...

A) 15 B) 18 C) 21 D) 24

Correct answer: B) 18 Why the distractors fail: - A) 15 is an incorrect answer because it does not follow the pattern of the sequence. - C) 21 is an incorrect answer because it does not follow the pattern of the sequence. - D) 24 is an incorrect answer because it does not follow the pattern of the sequence.

MCQ 5 [F]

Create a sequence using the formula 4n - 2, where n is the term number. Find the first two terms of the sequence.

A) 2, 6 B) 4, 8 C) 6, 10 D) 8, 12

Correct answer: A) 2, 6 Why the distractors fail: - B) 4, 8 is an incorrect answer because it does not follow the pattern of the sequence. - C) 6, 10 is an incorrect answer because it does not follow the pattern of the sequence. - D) 8, 12 is an incorrect answer because it does not follow the pattern of the sequence.

Short-answer questions

1. Create a sequence using the formula 5n - 3, where n is the term number. Find the first three terms of the sequence.
2. Find the next term in the sequence 2, 5, 8, 11, ...
3. What is the formula for the sequence 3, 6, 9, 12, ...?
4. Create a sequence using the formula 2n + 3, where n is the term number. Find the first two terms of the sequence.
5. Find the formula for the sequence 2, 4, 6, 8, ...