Year 6 Maths reasoning (SATs) · Algebra and sequences · Lesson 7.1

Year 6 Maths reasoning (SATs): Linear sequences and missing terms

Part of the Year 6 Maths reasoning (SATs) algebra and sequences chapter. Chapter overview · whole chapter on one page

7.1

Linear sequences and missing terms

Year 6
Generate and describe linear number sequences, including the term-to-term rule in words (Year 5-6), Find missing terms in sequences, including sequences that go up and down (Year 5-6)

Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.

Story. Priya is saving money for a school trip. She saves 5 pounds in the first week, 9 pounds in the second, 13 pounds in the third, and she wants to know how much she saves each week, so she can work out the next amounts.

Rule

A linear sequence goes up or down by the same amount each time. That amount is the difference.

The term-to-term rule says how to get from one term to the next, for example "add 4" or "subtract 3".

Key ideas

The difference is the same between every pair of terms in a linear sequence.
A sequence can go down: 20, 16, 12, 8 has the rule "subtract 4".
Check the rule on every pair of terms before you use it.

Worked example 7.1.1

The sequence starts 5, 9, 13, 17, ... Write the next term.

Method. Find the difference between terms, then apply it again.

Find the rule. Each term is the one before with add 4.
9 - 5 = 4
Apply the rule to the last term. Take the last term, 17, and add 4.
17 + 4 = 21
Write the answer.
21

Check. 21 - 17 = 4. ✓

Watch out. Check the difference between every pair of terms, not just the first two.

Worked example 7.1.2

Find the missing term: 10, 7, __, 1, -2.

Method. Find the difference between the known terms, then count to the gap.

Find the difference. The terms go subtract 3 each time.
difference = -3
Work out the missing term. Count from a known term to the gap.
10 - 6 = 4
Write the answer.
4

Check. 4 is in the same pattern: the difference is -3. ✓

Watch out. The term is missing from the list, so count the steps carefully.

Worked example 7.1.3

The sequence starts 30, 24, 18, 12, ... Write the next term.

Method. Find the difference between terms, then apply it again.

Find the rule. Each term is the one before with subtract 6.
24 - 30 = -6
Apply the rule to the last term. Take the last term, 12, and subtract 6.
12 - 6 = 6
Write the answer.
6

Check. 6 - 12 = -6. ✓

Watch out. Check the difference between every pair of terms, not just the first two.

Watch out

Watch out. Check the difference between every pair of terms. A sequence with a missing term may look wrong until you check.

Exam tip

Practice guide. Write the difference between two neighbouring terms above the sequence, then count it along.

Exercise 7A Practice: linear sequences and missing terms

Non-calculator

FThe sequence starts 3, 8, 13, 18, ... Write the next term.

Done

FThe sequence starts 20, 16, 12, 8, ... Write the next term.

Done

FThe sequence starts 1, 8, 15, 22, ... Write the next term.

Done

PSThe sequence starts 100, 92, 84, 76, ... Write the next term.

Done

FFind the missing term: 4, 10, __, 22, 28.

Done

FFind the missing term: 40, __, 30, 25, 20.

Done

FFind the missing term: 7, 16, 25, 34, __.

Done

FThe term-to-term rule for a sequence is "add 7". The first term is 12. Write the second and third terms.

Done

PSThe term-to-term rule is "subtract 6". The fourth term is 9. What is the first term?

Done

RExplain how you know that the sequence 3, 8, 13, 18 goes up by 5 each time.

Done

FWhich is the correct term-to-term rule for 2, 6, 10, 14? Choose one: add 4, add 2 or multiply by 2.

Done

RTick the sequences that go up in equal steps. Options: 2, 4, 6, 8 | 1, 3, 6, 10 | 5, 10, 15, 20 | 3, 5, 9, 11. Write the options you would tick, in the order given.

Done

PSA sequence goes 50, 46, 42, __, 34. Find the missing term.

Done

PSA bike shop changes the price of a bike by the same amount each week. It costs 240 pounds in week 1, 225 pounds in week 2 and 210 pounds in week 3. Write the price in week 5.

Done