Patterns in Mathematics — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Patterns in Mathematics" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Patterns in Mathematics" — 8 important questions with detailed answers for CBSE boa…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 6 Mathematics — Patterns in Mathematics. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Patterns in Mathematics — All 8 Questions Solved
Q1. What is the next number in the pattern: 2, 4, 6, 8, 10, ___?
This is a sequence where each number increases by 2.
Step 1: Find the difference between consecutive numbers
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
Step 2: The pattern is "add 2 to get the next number"
Step 3: 10 + 2 = 12
Answer: 12
Q2. Write the next three numbers in the pattern: 5, 10, 15, 20, ___?
This is a sequence where each number increases by 5 (multiples of 5).
Step 1: Find the difference between consecutive numbers
10 - 5 = 5
15 - 10 = 5
Step 2: The pattern rule is "add 5 each time"
Step 3: Continue the pattern
20 + 5 = 25
25 + 5 = 30
30 + 5 = 35
Answer: 25, 30, 35
Q3. What comes next in the pattern: 1, 1, 2, 3, 5, 8, ___?
This is the Fibonacci pattern where each number is the sum of the two numbers before it.
Step 1: Check if each number = previous two numbers added
1 + 1 = 2 ✓
1 + 2 = 3 ✓
2 + 3 = 5 ✓
3 + 5 = 8 ✓
Step 2: Apply the rule to find the next number
The two numbers before are 5 and 8
Step 3: 5 + 8 = 13
Answer: 13
Q4. Find the missing number in the pattern: 3, 6, 9, ___, 15, 18
This is a sequence of multiples of 3.
Step 1: Find the pattern by checking differences
6 - 3 = 3
9 - 6 = 3
Step 2: Each number increases by 3
Step 3: The missing number is
9 + 3 = 12
Step 4: Check: 12 + 3 = 15 ✓ and 15 + 3 = 18 ✓
Answer: 12
Q5. What is the rule for the pattern: 2, 4, 8, 16, 32? Write the rule in words.
This is a pattern where each number is multiplied by 2.
Step 1: Check the relationship between consecutive numbers
4 ÷ 2 = 2
8 ÷ 4 = 2
16 ÷ 8 = 2
32 ÷ 16 = 2
Step 2: Each number is 2 times the previous number
Answer: The rule is "multiply the previous number by 2" or "each term is double the term before it"
Q6. Complete the pattern: 100, 90, 80, 70, ___, ___, ___
This is a decreasing pattern where each number decreases by 10.
Step 1: Find the difference between consecutive numbers
90 - 100 = -10
80 - 90 = -10
70 - 80 = -10
Step 2: The rule is "subtract 10 from the previous number"
Step 3: Continue the pattern
70 - 10 = 60
60 - 10 = 50
50 - 10 = 40
Answer: 60, 50, 40
Q7. What is the 7th number in the pattern: 1, 4, 7, 10, 13, ...?
This is an arithmetic sequence where each number increases by 3.
Step 1: Find the difference between consecutive numbers
4 - 1 = 3
7 - 4 = 3
10 - 7 = 3
Step 2: The pattern increases by 3 each time
Step 3: The given numbers are the 1st through 5th terms
1st: 1
2nd: 4
3rd: 7
4th: 10
5th: 13
6th: 13 + 3 = 16
7th: 16 + 3 = 19
Answer: 19
Q8. Write the pattern rule for: 11, 12, 14, 17, 21, ... (Hint: look at the differences)
This pattern is based on the differences between consecutive numbers.
Step 1: Find the first set of differences
12 - 11 = 1
14 - 12 = 2
17 - 14 = 3
21 - 17 = 4
Step 2: The differences form a pattern: 1, 2, 3, 4, ...
Step 3: Each difference increases by 1
Answer: The pattern rule is "the differences between consecutive numbers increase by 1 each time" (differences are 1, 2, 3, 4, 5, ...)
Patterns in Mathematics — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What is the next number in the pattern: 2, 4, 6, 8, __?
- A. 9
- B. 10
- C. 11
- D. 12
Answer: B. 10 — This pattern consists of even numbers, where each number is 2 more than the previous one. So, 8 + 2 = 10.
MCQ 2. Find the missing number in the sequence: 25, 20, 15, __, 5.
- A. 10
- B. 12
- C. 13
- D. 14
Answer: A. 10 — Each number in the pattern is 5 less than the previous number. Following this rule, 15 - 5 = 10.
MCQ 3. Which shape comes next in the pattern: Circle, Square, Triangle, Circle, Square, __?
- A. Circle
- B. Square
- C. Triangle
- D. Rectangle
Answer: C. Triangle — The pattern repeats a sequence of three shapes: Circle, Square, Triangle. After 'Circle, Square', the next shape is Triangle.
MCQ 4. What is the next term in the sequence: 3, 6, 9, 12, __?
- A. 14
- B. 15
- C. 16
- D. 18
Answer: B. 15 — This pattern shows multiples of 3, increasing by 3 each time. So, 12 + 3 = 15.
MCQ 5. What comes next in the pattern: 1, 5, 2, 6, 3, 7, __?
- A. 4
- B. 8
- C. 9
- D. 10
Answer: A. 4 — This pattern has two interleaved sequences: (1, 2, 3, ...) and (5, 6, 7, ...). The next number in the first sequence is 4.
MCQ 6. Identify the next number in the pattern: 1, 4, 9, 16, __.
- A. 20
- B. 25
- C. 30
- D. 36
Answer: B. 25 — This pattern consists of perfect squares: 1x1, 2x2, 3x3, 4x4. The next number will be 5x5 = 25.
MCQ 7. Find the missing number: 10, 22, 34, __, 58.
- A. 42
- B. 44
- C. 46
- D. 48
Answer: C. 46 — Each number in the pattern is 12 more than the previous number. To find the missing term, add 12 to 34, which is 46.
MCQ 8. What is the next number in the sequence: 1, 1, 2, 3, 5, 8, __?
- A. 10
- B. 11
- C. 12
- D. 13
Answer: D. 13 — This is the Fibonacci sequence, where each number is the sum of the two preceding ones. So, 5 + 8 = 13.
MCQ 9. A pattern shows 1 dot, then 3 dots, then 6 dots. How many dots will be in the next figure if the pattern continues?
- A. 8
- B. 9
- C. 10
- D. 12
Answer: C. 10 — This pattern represents triangular numbers: 1 (1), 3 (1+2), 6 (1+2+3). The next term will be 1+2+3+4 = 10.
MCQ 10. What is the next number in the pattern: 1, 2, 4, 7, 11, __?
- A. 13
- B. 15
- C. 16
- D. 17
Answer: C. 16 — The difference between consecutive numbers increases by 1 each time: +1, +2, +3, +4. The next difference should be +5, so 11 + 5 = 16.
MCQ 11. Find the missing term in the sequence: A1, B2, C3, __, E5.
- A. D3
- B. D4
- C. E4
- D. C4
Answer: B. D4 — The pattern follows consecutive letters of the alphabet and consecutive numbers. After C3, the next term is D4.
MCQ 12. What is the next number in the sequence: 3, 7, 15, 31, 63, __?
- A. 125
- B. 126
- C. 127
- D. 128
Answer: C. 127 — The pattern follows the rule: (previous number × 2) + 1. So, (63 × 2) + 1 = 126 + 1 = 127.
MCQ 13. Find the next term in the series: 100, 95, 85, 70, 50, __.
- A. 20
- B. 25
- C. 30
- D. 35
Answer: B. 25 — The difference between consecutive terms is increasing: -5, -10, -15, -20. The next difference will be -25, so 50 - 25 = 25.
MCQ 14. What is the next number in the pattern: 2, 6, 12, 20, 30, __?
- A. 32
- B. 36
- C. 40
- D. 42
Answer: D. 42 — The differences between consecutive terms are +4, +6, +8, +10. The next difference will be +12, so 30 + 12 = 42.
MCQ 15. A series follows the rule: Start with 2. Then, multiply by 3, subtract 1. What is the 5th term in the series: 2, 5, 14, 41, __?
- A. 120
- B. 121
- C. 122
- D. 123
Answer: C. 122 — The pattern is (previous term × 3) - 1. For the 5th term, apply this to 41: (41 × 3) - 1 = 123 - 1 = 122.
MCQ 16. What is the next number in the sequence: 2, 4, 6, 8, ___?
- A. 9
- B. 10
- C. 11
- D. 12
Answer: B. 10 — This is a pattern of even numbers, where each number is obtained by adding 2 to the previous number. So, 8 + 2 = 10.
MCQ 17. Identify the rule for the following pattern: 5, 10, 15, 20, ...
- A. Subtract 5
- B. Add 5
- C. Multiply by 2
- D. Divide by 5
Answer: B. Add 5 — Each number in the sequence is obtained by adding 5 to the previous number. For example, 5 + 5 = 10, 10 + 5 = 15.
MCQ 18. Complete the sequence: 100, 90, 80, ___, 60.
- A. 75
- B. 70
- C. 65
- D. 85
Answer: B. 70 — This is a decreasing pattern where each number is obtained by subtracting 10 from the previous number. So, 80 - 10 = 70.
MCQ 19. What comes next in the visual pattern: Circle, Square, Triangle, Circle, Square, ___?
- A. Square
- B. Circle
- C. Triangle
- D. Rectangle
Answer: C. Triangle — The pattern repeats the sequence of shapes: Circle, Square, Triangle. After 'Square', 'Triangle' should follow.
MCQ 20. If the pattern is 'add 3', and the first number is 7, what is the 3rd number in the sequence?
- A. 10
- B. 13
- C. 16
- D. 19
Answer: B. 13 — The first number is 7. Adding 3 gives the second number: 7 + 3 = 10. Adding 3 again gives the third number: 10 + 3 = 13.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.