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Concept 1 of 6

Number Series: Find the Next Number

1

Today's big idea

Write the gap under every pair, and equal gaps mean you add that gap once more.

One gap is never enough to trust, so check them all before you name the rule.

2

How it works

👀 What's going on?

Ravi adds 4 stickers to his album every week. Week by week his total reads 4, 8, 12, 16. He never has to ask what Week 5 brings, because the gap already told him.

💡 Here's the trick

Find the gap, then add it again246810+2+2+2+2All gaps equal +2 → add 2 again8 + 2 = 10Equal gaps → ADD · Each one doubled → ×2

Look at the row of numbers above. Under every pair sits the same jump, +2. When every gap matches, the rule is simply add that gap. Name the gap and the next number is one small sum away: 8 + 2 = 10.

🪄 How to do it

  1. 1.Write the gap under each pair in the series above.
  2. 2.Check whether every gap is the same, or whether they take turns.
  3. 3.Add the gap to the last number you were given.

✍️ Try it

  1. 1.What is the next number in 6, 11, 16, 21, ?
  2. 2.What is the next number in 30, 26, 22, 18, ?

Series 1 climbs by 5 every time, so the next number is 21 + 5 = 26. Series 2 travels the other way. Its gaps are −4, −4, −4, so the next number is 18 − 4 = 14.

⚠️ Watch out

You might be thinking one gap is enough to name the rule. Look at 3, 5, 10, 12, ? and stop at the first gap. It is +2, so 12 + 2 = 14 looks safe. But notice that the gaps run +2, +5, +2, so the next gap is +5. The real answer is 12 + 5 = 17. Series that swap between two gaps are the tricky ones.

🌟 Why this matters

Spotting a gap is how you guess when the next bus arrives. It is how you know what your money box will hold by Sunday. It is even how you find your row of seats in a hall. Name the gap once and the rest follows.
Exam tip: Number series open the reasoning section on nearly every Class 3 paper, so check two gaps before you answer.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Find the next number: 3, 9, 15, 21, ?”

  1. 1

    Write the gaps

    9−3 = +6. 15−9 = +6. 21−15 = +6.

  2. 2

    Spot the rule

    Every gap is +6. Equal gaps → add the same number again.

  3. 3

    Apply it once more

    21 + 6 = 27

  4. 4

    Answer ✓

    Next = 27

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Reveal the jumps between the numbers, spot the rule, then extend the series.

SERIES · ROUND 1 OF 3

2+2
4+2
6+2
8
?
5

Quick check

✅ VERIFICATION

Find the missing number: 14, ?, 26, 32, 38

⚡ Finish the activity above first to answer.

Keep going!

Up next: Pattern Completion

Shortest repeating group = the core.

Concept 2 of 6 →