Extra Questions for Class 6 Maths Chapter 1: Patterns in Mathematics

Fresh practice questions for Class 6 Maths Chapter 1 “Patterns in Mathematics”, reinforcing number and shape sequences. These Class 6 Mathematics Chapter 1 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Q1. Find the next three terms of the sequence: 2, 5, 10, 17, 26, …

Answer: The differences are 3, 5, 7, 9 (increasing by 2 each time — these are consecutive odd numbers). So the next differences are 11, 13, 15: 26+11=37, 37+13=50, 50+15=65. Next three terms: 37, 50, 65. (This is actually the sequence n²+1: 1²+1=2, 2²+1=5, 3²+1=10, …, 6²+1=37 ✓.)

Q2. Assertion-Reason — Assertion (A): The sum of the first 20 odd numbers is 400. Reason (R): The sum of the…

Assertion (A): The sum of the first 20 odd numbers is 400.
Reason (R): The sum of the first n odd numbers is always n².

Answer: Both A and R are true, and R correctly explains A. 20²=400.

Q3. Is 100 a triangular number? Justify your answer.

Answer: Solve n(n+1)/2=100 ⇒ n(n+1)=200. Testing n=13: 13×14=182 (too small). n=14: 14×15=210 (too big). Since no whole number n satisfies this exactly, 100 is not a triangular number.

Q4. Spot the Error — A student claims: "The number of connecting lines in a complete graph of n points is…

A student claims: “The number of connecting lines in a complete graph of n points is n(n+1)/2.” Check this against a complete graph of 3 points (a triangle), which has 3 connecting lines, and correct the formula if needed.

Answer: Testing n=3 in n(n+1)/2 gives 3×4/2=6, which does not match the actual 3 lines. The correct formula is n(n-1)/2: for n=3, 3×2/2=3 ✓, matching the triangle’s 3 sides.

Q5. What is the 12th triangular number, and what is the 12th square number? Which is larger?

Answer: 12th triangular number = 12×13/2 = 78. 12th square number = 12² = 144. The square number (144) is larger.

Q6. HOTS — Using the identity "sum of first n cubes = (sum of first n counting numbers)²," find…

Using the identity “sum of first n cubes = (sum of first n counting numbers)²,” find 1³+2³+3³+4³+5³ without adding the cubes directly.

Answer: Sum of first 5 counting numbers = 1+2+3+4+5=15. So the sum of the first 5 cubes = 15² = 225. (Check by direct addition: 1+8+27+64+125=225 ✓.)

Q7. What is the 7th Virahanka number, given the sequence starts 1, 2, 3, 5, 8, …?

Answer: Continuing the recurrence (each term = sum of the two before it): 1, 2, 3, 5, 8, 13, 21. The 7th term is 21.

Q8. How many little squares are in a 9×9 stacked-squares arrangement, and how many little triangles are in the corresponding 9-row stacked-triangles arrangement?

Answer: Stacked squares: 9² = 81. Stacked triangles (sum of first 9 odd numbers): 1+3+5+7+9+11+13+15+17 = 81 as well — both give the same total, since both are square-number sequences.

Q9. Find the next hexagonal number after 91 (the sequence is 1, 7, 19, 37, 61, 91, …).

Answer: The differences increase by 6 each time: 6,12,18,24,30 so far, so the next difference is 36: 91+36=127.

Q10. How many total line segments would a Koch snowflake have after 5 steps (starting from a triangle with 3 segments)?

Answer: Using 3×4ⁿ: after 5 steps, 3×4⁵ = 3×1024 = 3,072 line segments.

See also: NCERT Solutions for Class 6 Maths Chapter 1

Quick revision: Revision Notes for Class 6 Maths Chapter 1

Frequently Asked Questions

What is the next number in the pattern 2, 4, 6, 8, and how do you know?
The next number is 10, since each term increases by a constant difference of 2, so continuing this rule by adding 2 to the last term, 8, gives the next term as 10.

How can visual patterns made of dots or shapes help in understanding number patterns?
Arranging dots or shapes in a growing sequence provides a visual way to see how a number pattern grows, making the underlying rule easier to notice and predict than looking at numbers alone.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.