Arithmetic
Constant difference (+/−) and simple growing number patterns.
Arithmetic
Arithmetic Number Series
What you'll learn
- Find the rule linking each number to the next.
- Constant difference — add or subtract the same amount.
- Skip counting patterns (+2, +5, −3).
- Olympiad-style step method for short series.
Key concepts
Level 1 — Core idea
Verbal: 5, 8, 11, 14 — say 'plus three each time.'
Symbolic: Gap d = a₂ − a₁; if all gaps equal → arithmetic series.
Visual: Number line jumps: +3 arrow between each term.
Level 2 — Going deeper
If gaps differ by same amount (2, 4, 6, 8 gaps) — second-level pattern (intro). Always verify rule on two pairs minimum.
NCERT anchor
NCERT Math Mela, Class 3 — Chapter 5 skip-counting supports series reasoning. Practice counting forwards and backwards.
Worked example
Next term: 2, 5, 8, 11, ?
Step 1 — Gaps: +3, +3, +3
Step 2 — Rule: add **3**
Step 3 — 11 + 3 = **14**
Missing middle: 10, ?, 18, 22 (add 4)
Step 1 — Gap 18 to 22 = +4
Step 2 — Work backwards: 18 − 4 = 14; 10 to 14 = +4
Answer: **14** ✓
Common mistakes
| Mistake | Why | Fix |
|---|---|---|
| Random +1 guess | No gap check | Write all gaps first |
| One gap only | Off-by-one | Verify on two pairs |
| Adding when series falls | Direction ignored | Try subtract if numbers shrink |
| Copy last number | 19, 19 pattern | Apply rule each step |
Quick check
- Next: 10, 15, 20, 25, ?
- Rule for 4, 6, 8, 10?
- Missing: 3, ?, 7, 9
- Stretch: Series: 1, 4, 7, 10 — what is 10th term? (add 3 nine times)
Revision tip: Underline gaps between numbers before picking the next term.
Open the Practice tab for graded questions on Arithmetic Number Series.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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