Number Series

• How to spot the rule connecting numbers in a series: same step, growing step, or alternating steps.
• How to use the rule to predict the next number in the pattern.
• A simple 3-step method: find gaps, check if gaps repeat/grow, then apply the rule once more.

Level 1 — Constant difference series

Verbal: Every term is made by adding (or subtracting) the same number each time.

Symbolic: 3, 7, 11, 15, ? — each term is previous + 4, so next = 15 + 4 = 19.

Level 2 — Growing-gap series

Verbal: The gap between terms itself increases by a fixed amount each time (e.g. +2, +3, +4).

Real-life: Saving pocket money where you save Rs 2 more than last week, every week.

Level 3 — Alternating rule series

Verbal: The rule switches between two operations, such as +5, -2, +5, -2, ...

Find the next number: 4, 8, 12, 16, ?

Step 1 - Find gaps: 8-4=4, 12-8=4, 16-12=4
Step 2 - Gap is constant at 4
Step 3 - Next term = 16 + 4 = 20
Answer: 20

Find the next number: 1, 3, 6, 10, ?

Step 1 - Gaps: 3-1=2, 6-3=3, 10-6=4
Step 2 - Gap grows by 1 each time, so next gap = 5
Step 3 - Next term = 10 + 5 = 15
Answer: 15

• What is the next number after 5, 10, 15, 20?
• In 2, 5, 9, 14, ? what is the pattern of gaps?
• Is 30, 24, 18, 12 an increasing or decreasing series?
• Stretch: Find the next two numbers in 1, 2, 4, 7, 11, ?, ?

Revision tip: Always write the gap under each pair of numbers before guessing the answer.

Open the Practice tab for graded questions on Number Series.