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Class 6 Maths: Patterns in Mathematics, 8 practice questions with answers

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These are 8 practice questions on Chapter 1, Patterns in Mathematics, of the new NCERT Class 6 Maths textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover continuing a number sequence and stating its rule, sums of even numbers, odd numbers added up and back down, triangular numbers, running sums of the Virahanka numbers, the diagonals of regular polygons, pentagonal numbers, and numbers that are both squares and cubes. For a walk-through of the chapter itself, see our Class 6 Maths Chapter 1 explainer. Try each question on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, and none of the chapter's own exercises is reused or turned round. No practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 1, printed pages 1 to 12):

Number sequences

Question 1. Write the next three numbers in each sequence and state its rule: (a) 2, 5, 8, 11, …; (b) 1, 5, 25, …; (c) 3, 7, 13, 21, 31, …

Answer: (a) 14, 17, 20; (b) 125, 625, 3125; (c) 43, 57, 73. (a) Each number is 3 more than the one before. (b) Each number is 5 times the one before: these are the powers of 5. (c) The gaps are 4, 6, 8, 10, going up by 2 each time, so the next gaps are 12, 14 and 16, giving 31 + 12 = 43, 43 + 14 = 57 and 57 + 16 = 73. Another way to see it: each number is one more than a counting number times the next one: 1 × 2 + 1 = 3, 2 × 3 + 1 = 7, and so on, so the next is 6 × 7 + 1 = 43. (Number sequences and their rules, pages 2 and 3.)

Question 2. Add up the even numbers in order: 2, then 2 + 4, then 2 + 4 + 6, then 2 + 4 + 6 + 8. (a) What numbers do you get, and what are the next two? (b) Draw 2 + 4 + 6 as dots. What shape can the dots make, and why? (c) Use the pattern to find 2 + 4 + 6 + … + 20 without adding term by term.

Answer: (a) 2, 6, 12, 20, then 30 and 42; (b) a rectangle of 3 rows of 4; (c) 110. (a) 2 = 1 × 2, 6 = 2 × 3, 12 = 3 × 4 and 20 = 4 × 5, so the next two are 5 × 6 = 30 and 6 × 7 = 42. (b) Each even number is twice a counting number, so 2 + 4 + 6 is twice 1 + 2 + 3, which is two copies of the triangle of 6 dots. Turn one triangle upside down and fit it against the other: they make a rectangle 3 dots by 4 dots, 12 in all. (c) 2 + 4 + … + 20 adds 10 even numbers, so it is a rectangle 10 by 11: 10 × 11 = 110. Check: it is twice 1 + 2 + … + 10 = 55. (Adding up a sequence and explaining it with a dot picture, pages 6 to 8; triangular numbers, page 3.)

Question 3. Add the odd numbers up and then back down: 1, then 1 + 3 + 1, then 1 + 3 + 5 + 3 + 1, then 1 + 3 + 5 + 7 + 5 + 3 + 1. (a) What totals do you get? (b) Find the next two. (c) Draw the third one as rows of dots, one row for each number, centred under each other. What shape is it, and how does it split into two squares?

Answer: (a) 1, 5, 13, 25; (b) 41 and 61; (c) a diamond, which splits into a 3 × 3 square and a 2 × 2 square. (a) 1; 1 + 3 + 1 = 5; 1 + 3 + 5 + 3 + 1 = 13; 1 + 3 + 5 + 7 + 5 + 3 + 1 = 25. (b) The odd numbers going up add to a square, and the ones coming back down add to the square before it. The next total goes up to 9: 1 + 3 + 5 + 7 + 9 = 25 and then 7 + 5 + 3 + 1 = 16, so 41. The one after goes up to 11: 36 + 25 = 61. (c) Rows of 1, 3, 5, 3 and 1 dots, centred, make a diamond. Tilt the page so the diamond stands on a corner: every other dot belongs to a tilted 3 × 3 square of 9 dots, and the dots in its gaps make a tilted 2 × 2 square of 4 dots, so 9 + 4 = 13. (Adding odd numbers gives squares, pages 6 and 7; dot pictures of sequences, pages 3 to 5.)

Question 4. Is 55 a triangular number? Is 50? Explain.

Answer: 55 is; 50 is not. Triangular numbers are the sums 1, 1 + 2, 1 + 2 + 3, and so on. 1 + 2 + … + 10 = 55, so 55 dots make a triangle with rows of 1 to 10. The triangular numbers just below and above 50 are 1 + … + 9 = 45 and 1 + … + 10 = 55, so 50 is not triangular: 50 dots cannot make a full triangle. (Triangular numbers, pages 3 to 5.)

Relations between sequences

Question 5. The Virahanka numbers are 1, 2, 3, 5, 8, 13, 21, 34, …, each one the sum of the two before it. (a) Add them up as you go: 1, 1 + 2, 1 + 2 + 3, and so on up to 1 + 2 + 3 + 5 + 8 + 13. What running totals do you get? (b) Compare each running total with the Virahanka number two places further on. What do you notice? (c) Why does it keep happening?

Answer: (a) 1, 3, 6, 11, 19, 32; (b) each total is 2 less than the Virahanka number two places on; (c) see below. (a) 1; 1 + 2 = 3; 3 + 3 = 6; 6 + 5 = 11; 11 + 8 = 19; 19 + 13 = 32. (b) The sum of the first one, 1, is 2 less than 3; the sum of the first two, 3, is 2 less than 5; then 6 and 8, 11 and 13, 19 and 21, and 32 and 34. Each running total is 2 less than the Virahanka number two places further on. (c) Suppose a running total is 2 less than some Virahanka number. The next number you add is the one just before that Virahanka number, and adding the two neighbours gives the following Virahanka number. So the new total is again 2 less than a Virahanka number, one place further on, and the pattern carries on for ever. (Virahanka numbers, page 3; relations among number sequences, pages 6 to 9.)

Question 6. A diagonal of a shape joins two corners that are not next to each other. (a) How many diagonals do a triangle, a square, a regular pentagon and a regular hexagon have? (b) Find the numbers for the next two regular polygons, the heptagon and the octagon. (c) Describe the jumps, and explain them.

Answer: (a) 0, 2, 5, 9; (b) 14 and 20; (c) the jumps are 2, 3, 4, 5, 6. (a) A triangle has 0 diagonals, a square 2, a pentagon 5 and a hexagon 9. (b) Each corner joins to every corner except itself and its two neighbours. A heptagon has 7 corners, each with 7 − 3 = 4 diagonals, and each diagonal has two ends, so 7 × 4 ÷ 2 = 14. An octagon: 8 × 5 ÷ 2 = 20. (c) From 0 to 2 to 5 to 9 to 14 to 20, the jumps are 2, 3, 4, 5, 6. When a new corner is added, it can be joined to every old corner except its two neighbours, and the old side between those two neighbours becomes a diagonal as well. So a hexagon gains 6 − 2 = 4 new diagonals, plus 1 old side, when it becomes a heptagon: 9 + 5 = 14. Check: diagonals plus sides gives the lines of the complete graph on the same corners; for the hexagon, 9 + 6 = 15 = 1 + 2 + 3 + 4 + 5. (Regular polygons and complete graphs, pages 10 and 11.)

Question 7. The pentagonal numbers are 1, 5, 12, 22, …. Each picture is a pentagon of dots, and each new pentagon is drawn bigger than the last, sharing one corner with it. (a) Find the jumps between the numbers. (b) Find the next two pentagonal numbers. (c) What is the rule for the jumps?

Answer: (a) 4, 7, 10; (b) 35 and 51; (c) the jumps go up by 3 each time. (a) 5 − 1 = 4, 12 − 5 = 7 and 22 − 12 = 10. (b) The jumps go up by 3, so the next jumps are 13 and 16: 22 + 13 = 35 and 35 + 16 = 51. (c) Each new pentagon adds 3 new sides of dots (the other 2 sides run along the old pentagon), and each of those sides is 1 dot longer than last time, so the jump is 3 more each time. (Shape sequences and their number sequences, pages 9 to 12.)

Question 8. Which numbers up to 1000 are both square numbers and cube numbers?

Answer: 1, 64 and 729. The cubes up to 1000 are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. Check which of them are squares: 1 = 1 × 1, 64 = 8 × 8 (and 4 × 4 × 4), and 729 = 27 × 27 (and 9 × 9 × 9). None of the others is a square. (Squares and cubes, pages 3 and 4.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Patterns in Mathematics, Class 6 worksheet. Printable, in English, Hindi and Marathi, with an answer key.