Maths

Number Sequences

Class 3

🎯 Learning Objectives

Understand what a number sequence (pattern) is.
Identify increasing sequences that add a fixed number.
Identify decreasing sequences that subtract a fixed number.
Perform skip counting by 2s, 3s, 5s, 10s, and 100s.
Find the rule in a given number sequence.
Find missing numbers in a sequence.
Recognise growing patterns where the amount added increases.

📖 Introduction

Look at the house numbers on your street: 1, 3, 5, 7, 9... Do you notice something? Each number is 2 more than the one before it! This is called a number sequence — a list of numbers that follow a rule or pattern. Number sequences are everywhere — in cricket scores, festival countdowns, and even the pages of your textbook. Once you learn to spot the rule, you can predict what comes next!

What is a Number Sequence?

A number sequence is a list of numbers arranged in a special order. Each number in the sequence is called a term. The numbers follow a rule — a pattern that tells you how to get from one number to the next.

Example: 2, 4, 6, 8, 10, 12...
Rule: Add 2 each time.
Terms: 2 is the 1st term, 4 is the 2nd term, 6 is the 3rd term, and so on.

Every sequence has:

A starting number — where the sequence begins
A rule — what you do to get the next number
Terms — the numbers in the sequence

Increasing Sequences (Adding a Fixed Number)

In an increasing sequence, each number is bigger than the one before it. You get the next number by adding the same number every time.

Rule	Sequence	What Happens
Add 2	3, 5, 7, 9, 11, 13	Each number is 2 more
Add 3	4, 7, 10, 13, 16, 19	Each number is 3 more
Add 5	5, 10, 15, 20, 25, 30	Each number is 5 more
Add 10	10, 20, 30, 40, 50, 60	Each number is 10 more
Add 4	1, 5, 9, 13, 17, 21	Each number is 4 more

Real-life example: Arjun saves ₹5 every day.
Day 1: ₹5, Day 2: ₹10, Day 3: ₹15, Day 4: ₹20, Day 5: ₹25...
Rule: Add 5. This is an increasing sequence!

Decreasing Sequences (Subtracting a Fixed Number)

In a decreasing sequence, each number is smaller than the one before it. You get the next number by subtracting the same number every time.

Rule	Sequence	What Happens
Subtract 2	20, 18, 16, 14, 12, 10	Each number is 2 less
Subtract 3	30, 27, 24, 21, 18, 15	Each number is 3 less
Subtract 5	50, 45, 40, 35, 30, 25	Each number is 5 less
Subtract 10	100, 90, 80, 70, 60, 50	Each number is 10 less
Subtract 4	40, 36, 32, 28, 24, 20	Each number is 4 less

Real-life example: Diwali countdown! There are 10 days left for Diwali.
Day 1: 10 days left, Day 2: 9 days left, Day 3: 8 days left...
Rule: Subtract 1. This is a decreasing sequence!

Think: A rocket launch countdown goes 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0... Blast off! What is the rule? (Subtract 1)

Skip Counting Patterns

Skip counting means counting forward by jumping over numbers. Instead of counting 1, 2, 3, 4... you skip some numbers and count by a fixed amount.

Skip Counting by 2s

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...

These are all even numbers! You jump over one number each time.

Skip Counting by 3s

3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

This is the same as the 3 times table!

Skip Counting by 5s

5, 10, 15, 20, 25, 30, 35, 40, 45, 50...

Notice: the numbers always end in 0 or 5.

Skip Counting by 10s

10, 20, 30, 40, 50, 60, 70, 80, 90, 100...

The numbers always end in 0. Easy to remember!

Skip Counting by 100s

100, 200, 300, 400, 500, 600, 700, 800, 900, 1000

Just the hundreds! Like counting ₹100 notes.

Cricket connection: In a cricket match, if a batsman scores 4 runs on every ball:
Ball 1: 4 runs, Ball 2: 8 runs, Ball 3: 12 runs, Ball 4: 16 runs...
That's skip counting by 4s!

Staircase pattern showing number sequence increasing by 3 at each step

Finding the Rule in a Sequence

To find the rule, look at the difference between each pair of numbers next to each other.

Example 1: 7, 11, 15, 19, 23
11 − 7 = 4, 15 − 11 = 4, 19 − 15 = 4, 23 − 19 = 4
Rule: Add 4

Example 2: 45, 40, 35, 30, 25
45 − 40 = 5, 40 − 35 = 5, 35 − 30 = 5, 30 − 25 = 5
Numbers are getting smaller, so Rule: Subtract 5

Example 3: 100, 90, 80, 70, 60
100 − 90 = 10, 90 − 80 = 10
Rule: Subtract 10

Steps to find the rule:

Look at the first two numbers. Find the difference.
Check if the same difference works for the next pair.
If numbers go up → the rule is "Add ___"
If numbers go down → the rule is "Subtract ___"

Finding Missing Numbers

Once you know the rule, you can find any missing number in a sequence!

Example 1: 5, 10, ___, 20, 25
Rule: Add 5. So the missing number is 10 + 5 = 15

Example 2: 36, 33, 30, ___, 24
Rule: Subtract 3. So the missing number is 30 − 3 = 27

Example 3: 8, ___, 16, 20, 24
Rule: Add 4. So the missing number is 8 + 4 = 12

Example 4: 100, 200, ___, 400, ___
Rule: Add 100. Missing numbers: 300 and 500

Tip: Always check your answer! After filling in the missing number, make sure the rule still works for all the numbers around it.

Growing Patterns (Increasing Amounts)

In a growing pattern, the amount you add increases each time. The difference between numbers is not the same — it grows!

Example 1: 1, 2, 4, 7, 11, 16...
Differences: +1, +2, +3, +4, +5
The amount added grows by 1 each time!

Example 2: 2, 4, 8, 14, 22...
Differences: +2, +4, +6, +8
The amount added grows by 2 each time!

Example 3: 5, 6, 8, 11, 15, 20...
Differences: +1, +2, +3, +4, +5
Next difference would be +6, so next term = 20 + 6 = 26

Growing patterns are trickier because the rule changes! You need to look at how the differences themselves are changing.

Number Sequences in Daily Life (Indian Context)

Number sequences are all around us! Here are some examples from everyday life in India:

Situation	Sequence	Rule
House numbers (odd side)	1, 3, 5, 7, 9, 11...	Add 2
House numbers (even side)	2, 4, 6, 8, 10, 12...	Add 2
Cricket overs (runs at 6 per over)	6, 12, 18, 24, 30...	Add 6
Saving ₹10 daily	₹10, ₹20, ₹30, ₹40...	Add 10
Diwali countdown (days left)	10, 9, 8, 7, 6, 5...	Subtract 1
Counting ₹5 coins	5, 10, 15, 20, 25...	Add 5
Floor numbers in a building	G, 1, 2, 3, 4, 5...	Add 1
Auto-rickshaw fare (₹25 start + ₹10/km)	₹25, ₹35, ₹45, ₹55...	Add 10

Think: Meena's mother buys 2 litres of milk every day. How many litres does she buy in 1 day, 2 days, 3 days, 4 days, 5 days? (2, 4, 6, 8, 10 — skip counting by 2!)

Number line showing skip counting by 5s with hops

📝 Key Words

Word	Meaning
Sequence	A list of numbers arranged in a special order following a rule
Term	Each number in a sequence
Rule	The pattern or operation that connects one term to the next
Increasing sequence	A sequence where numbers get bigger (add)
Decreasing sequence	A sequence where numbers get smaller (subtract)
Skip counting	Counting forward by jumping a fixed number each time
Growing pattern	A pattern where the amount added increases each time
Difference	The gap between two numbers next to each other

⭐ Key Points to Remember

A number sequence is a list of numbers that follow a rule.
In an increasing sequence, you ADD the same number each time.
In a decreasing sequence, you SUBTRACT the same number each time.
To find the rule, subtract each number from the next one.
Skip counting by 5s always gives numbers ending in 0 or 5.
Skip counting by 10s always gives numbers ending in 0.
In a growing pattern, the difference itself increases.
Always check your answer by applying the rule to all terms.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. What comes next: 10, 20, 30, 40, ___?

Counting by 10: 40 + 10 = 50.

2. What comes next: 100, 200, 300, ___?

Counting by 100: 300 + 100 = 400.

3. What is the missing number: 15, 20, ___, 30, 35?

Counting by 5: the number between 20 and 30 is 25.

4. What comes next: 50, 45, 40, 35, ___?

Counting down by 5: 35 − 5 = 30.

5. Counting by 2: 2, 4, 6, 8, 10, ___?

10 + 2 = 12.

6. Counting by 10: 20, 30, 40, 50, ___?

50 + 10 = 60.

7. Counting by 100: 200, 300, 400, ___?

400 + 100 = 500.

8. Counting by 3: 3, 6, 9, 12, 15, ___?

15 + 3 = 18.

✏️ Practice Questions

A. Fill in the Blanks (10)

1. 5, 10, 15, , 25, 30. (Rule: Add )

2. 40, 36, 32, , 24, 20. (Rule: Subtract )

3. 100, 200, 300, , 500. (Rule: Add )

4. 7, 14, 21, , 35, 42. (Rule: Add )

5. 50, 45, 40, , 30, 25. (Rule: Subtract )

6. 12, 15, 18, 21, , 27. (Rule: Add )

7. 90, 80, 70, , 50, 40. (Rule: Subtract )

8. 4, 8, 12, 16, , 24. (Rule: Add )

9. 1, 3, 6, 10, , 21. (Growing pattern: +2, +3, +4, +)

10. 500, 450, 400, , 300. (Rule: Subtract )

B. Choose the Correct Answer (MCQ - 5)

1. What is the rule for: 6, 12, 18, 24, 30?

a) Add 4b) Add 6c) Add 8

2. What comes next? 55, 50, 45, 40, ___

a) 30b) 35c) 38

3. Which is a decreasing sequence?

a) 3, 6, 9, 12b) 20, 16, 12, 8c) 1, 2, 4, 7

4. Skip counting by 10 from 30 gives:

a) 30, 40, 50, 60b) 30, 35, 40, 45c) 30, 33, 36, 39

5. In the sequence 2, 3, 5, 8, 12, the differences are:

a) +1, +2, +3, +4b) +2, +2, +2, +2c) +1, +1, +1, +1

C. Find the Rule and Next Two Numbers (5)

1. 8, 13, 18, 23, 28, ___, ___
Rule: _____________ Next two: _____, _____

2. 72, 64, 56, 48, 40, ___, ___
Rule: _____________ Next two: _____, _____

3. 150, 200, 250, 300, 350, ___, ___
Rule: _____________ Next two: _____, _____

4. 99, 90, 81, 72, 63, ___, ___
Rule: _____________ Next two: _____, _____

5. 1, 4, 9, 16, 25, ___, ___
Rule: _____________ Next two: _____, _____

D. True or False (5)

1. In the sequence 10, 20, 30, 40, the rule is "Add 10".

2. Skip counting by 5 gives: 5, 10, 14, 20, 25.

3. A decreasing sequence always subtracts the same number.

4. In a growing pattern, the difference between terms stays the same.

5. The sequence 100, 90, 80, 70 is a decreasing sequence.

E. Word Problems (5)

1. Ravi collects 3 stamps every week. He starts with 5 stamps. How many stamps will he have after 1, 2, 3, 4, and 5 weeks? Write the sequence.

2. A bus has 50 passengers. At each stop, 5 passengers get off. Write the number of passengers after each of the first 5 stops.

3. Sita counts her pocket money: ₹10, ₹20, ₹30, ₹40... If she continues, how much will she have on the 8th day?

4. The house numbers on one side of a street are: 101, 103, 105, 107... What is the 10th house number?

5. In a cricket match, India's score after each over is: 6, 14, 22, 30... What is the rule? What will the score be after the 6th over?

🎨 Activity: Create Your Own Sequences

Activity 1: Sequence Builder

Create your own number sequences! Follow these steps:

Pick a starting number (e.g., 7)
Pick a rule (e.g., Add 6)
Write the first 8 terms of your sequence
Give it to a friend and ask them to find the rule!

Activity 2: Sequence Hunt

Walk around your house or neighbourhood and find 3 real-life number sequences. Write them down:

House numbers on your street
Prices of items (₹5, ₹10, ₹15 packs)
Steps on a staircase (count by floors)
Pages in your textbook chapters

Activity 3: Growing Pattern Challenge

Start with 1. Add 1, then add 2, then add 3, then add 4... Write the first 10 numbers. What do you notice? (These are called triangular numbers!)

Want to review the lesson again?

Mathematics

Number Sequences

Class 3 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Understand what a number sequence (pattern) is.
Identify increasing and decreasing sequences.
Perform skip counting by 2s, 3s, 5s, 10s, and 100s.
Find the rule in a sequence and find missing numbers.
Recognise growing patterns where the amount added increases.

Introduction

A number sequence is a list of numbers that follow a rule or pattern. Each number is called a term. The rule tells you how to get from one number to the next. Example: 2, 4, 6, 8, 10 (Rule: Add 2). Number sequences are everywhere — house numbers, cricket scores, savings, and countdowns!

Increasing Sequences (Add a Fixed Number)

Add 2: 3, 5, 7, 9, 11, 13 Add 3: 4, 7, 10, 13, 16, 19
Add 5: 5, 10, 15, 20, 25, 30 Add 10: 10, 20, 30, 40, 50, 60
Example: Arjun saves ₹5 daily → ₹5, ₹10, ₹15, ₹20, ₹25 (Rule: Add 5)

Decreasing Sequences (Subtract a Fixed Number)

Subtract 2: 20, 18, 16, 14, 12, 10 Subtract 5: 50, 45, 40, 35, 30
Subtract 10: 100, 90, 80, 70, 60, 50
Example: Diwali countdown → 10, 9, 8, 7, 6, 5... (Rule: Subtract 1)

Skip Counting Patterns

By 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (even numbers!)
By 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
By 5s: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 (end in 0 or 5)
By 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (end in 0)
By 100s: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000

Finding the Rule

Steps: 1) Find the difference between consecutive numbers. 2) Check if it's the same. 3) If numbers go up → Add. If down → Subtract.
Example: 7, 11, 15, 19, 23 → Differences: 4, 4, 4, 4 → Rule: Add 4
Example: 45, 40, 35, 30 → Differences: 5, 5, 5 → Rule: Subtract 5

Finding Missing Numbers

5, 10, ___, 20, 25 → Rule: Add 5 → Missing: 15
36, 33, 30, ___, 24 → Rule: Subtract 3 → Missing: 27
100, 200, ___, 400, ___ → Rule: Add 100 → Missing: 300, 500

Growing Patterns

In a growing pattern, the amount added increases each time:
1, 2, 4, 7, 11, 16 → Differences: +1, +2, +3, +4, +5 (grows by 1 each time)
5, 6, 8, 11, 15, 20 → Differences: +1, +2, +3, +4, +5 → Next: 20 + 6 = 26

Number Sequences in Daily Life

Situation	Sequence	Rule
House numbers (odd side)	1, 3, 5, 7, 9, 11	Add 2
Cricket (6 runs/over)	6, 12, 18, 24, 30	Add 6
Saving ₹10 daily	₹10, ₹20, ₹30, ₹40	Add 10
Diwali countdown	10, 9, 8, 7, 6, 5	Subtract 1
Counting ₹5 coins	5, 10, 15, 20, 25	Add 5
Auto fare (₹25 + ₹10/km)	₹25, ₹35, ₹45, ₹55	Add 10

⭐ Key Points

A number sequence follows a rule. Each number is a term.
Increasing sequence: Add the same number each time.
Decreasing sequence: Subtract the same number each time.
To find the rule: look at the difference between consecutive terms.
Skip counting by 5s → numbers end in 0 or 5.
Skip counting by 10s → numbers end in 0.
Growing patterns: the difference itself increases.
Always verify by checking the rule works for all terms.

A. Fill in the Blanks (10)

1. 5, 10, 15, , 25, 30. (Rule: Add )

2. 40, 36, 32, , 24, 20. (Rule: Subtract )

3. 100, 200, 300, , 500. (Rule: Add )

4. 7, 14, 21, , 35, 42. (Rule: Add )

5. 50, 45, 40, , 30, 25. (Rule: Subtract )

6. 12, 15, 18, 21, , 27. (Rule: Add )

7. 90, 80, 70, , 50, 40. (Rule: Subtract )

8. 4, 8, 12, 16, , 24. (Rule: Add )

9. 1, 3, 6, 10, , 21. (Growing pattern: +2, +3, +4, +)

10. 500, 450, 400, , 300. (Rule: Subtract )

B. Choose the Correct Answer (MCQ - 5)

1. What is the rule for: 6, 12, 18, 24, 30?

a) Add 4b) Add 6c) Add 8

2. What comes next? 55, 50, 45, 40, ___

a) 30b) 35c) 38

3. Which is a decreasing sequence?

a) 3, 6, 9, 12b) 20, 16, 12, 8c) 1, 2, 4, 7

4. Skip counting by 10 from 30 gives:

a) 30, 40, 50, 60b) 30, 35, 40, 45c) 30, 33, 36, 39

5. In the sequence 2, 3, 5, 8, 12, the differences are:

a) +1, +2, +3, +4b) +2, +2, +2, +2c) +1, +1, +1, +1

C. Find the Rule and Next Two Numbers (5)

1. 8, 13, 18, 23, 28, ___, ___

2. 72, 64, 56, 48, 40, ___, ___

3. 150, 200, 250, 300, 350, ___, ___

4. 99, 90, 81, 72, 63, ___, ___

5. 1, 4, 9, 16, 25, ___, ___

D. True or False (5)

1. In the sequence 10, 20, 30, 40, the rule is "Add 10".

2. Skip counting by 5 gives: 5, 10, 14, 20, 25.

3. A decreasing sequence always subtracts the same number.

4. In a growing pattern, the difference between terms stays the same.

5. The sequence 100, 90, 80, 70 is a decreasing sequence.

E. Word Problems (5)

1. Ravi collects 3 stamps every week. He starts with 5 stamps. How many stamps will he have after 1, 2, 3, 4, and 5 weeks? Write the sequence.

2. A bus has 50 passengers. At each stop, 5 passengers get off. Write the number of passengers after each of the first 5 stops.

3. Sita counts her pocket money: ₹10, ₹20, ₹30, ₹40... How much will she have on the 8th day?

4. House numbers on one side of a street: 101, 103, 105, 107... What is the 10th house number?

5. India's cricket score after each over: 6, 14, 22, 30... What is the rule? Score after the 6th over?

Activity: Create Your Own Sequences

1. Pick a starting number and a rule. Write the first 8 terms:

2. Write a decreasing sequence starting from 60 (subtract 7):

3. Growing pattern: Start at 1. Add 1, then 2, then 3, then 4... Write 10 numbers:

4. Find 2 number sequences in your house or neighbourhood. Write them:

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