Number Sequences Made Simple – A Must-Know for 7+, 8+ & 11+ Success

Number sequences are like puzzles with a pattern. If your child can crack the code, they can conquer one of the most common and rewarding question types in reasoning and maths exams. Let’s show you how!

What Are Number Sequences?

They’re a list of numbers that follow a rule. Your job is to figure out what the rule is and either find the missing number or predict the next one. Think of it like a secret maths language!

Why Exams Love Them

These questions test how well your child can spot patterns, think logically, and apply number skills – all key abilities for entrance exams like 7+, 8+, and 11+.

Where We Use Sequences in Real Life

From days of the week to counting money and bus times – number patterns are everywhere. Learning them trains the brain to think fast and clearly.

Try These Examples

Level 1 (Beginner): 2, 4, 6, 8, ?
✅ Answer: 10 (Add 2)

Level 2 (Intermediate): 10, 7, 4, 1, ?
✅ Answer: -2 (Subtract 3, but not starting at 0)

Level 3 (Advanced): 1, 4, 9, 16, ?
✅ Answer: 25 (Square numbers: 1×1, 2×2, 3×3…)

Common Pitfalls

Mistake: Only looking at the difference between two numbers.
Tip: Check if it’s adding, subtracting, doubling, halving or even using square numbers.

Also Known As

Patterns, sequences, progressions, number chains

Advanced Twists

Harder versions might use alternating patterns or more than one rule – e.g., add 2, then subtract 1, and repeat. Stay sharp!

This is a precursor to algebraic equations, e.g. in Level 1

Level 1 (Beginner): 2, 4, 6, 8, ?
✅ Answer: 10 (Add 2) <- this is like x2 where x – the index of the sequence – so fifth in the sequence is 5 x 2 = 10 or 30th will be 30 x 2 = 60!

And in Level 2

Level 2 (Intermediate): 10, 7, 4, 1, ?
✅ Answer: -2 (Subtract 3) <- this is multiplying by -3. So we start with -3 x 1 (equals -3) plus 13.

There is another common question example here, we are not starting at 0, the first number is 10, in this case, we calculated the multiple of the x index and adjusted it. Note, this is also the same technique used to post on a graph – if we plotted this on a graph, it would be a straight line sloping downwards, which crosses the x axis at 13, isn’t it great how the same calculations are used in so many applications?

Therefore the equation here is 13-x3 – but the point is the more the children start visualising the sequences, the quicker they will be able to make the jump to why these equations make the sequencing calculation easier, also it is good to quickly checking afterwards or a cool trick to work out numbers way down the sequence 🪄.

Memory Tricks

Say the numbers out loud — sometimes your ears catch the pattern faster than your eyes.