The following exercises are arranged according to the CBSE assessment format, moving from short, direct questions to longer, reasoning-based ones. Attempt every section.

A. Multiple Choice Questions (1 mark each)

1.     What is the next term in the sequence 1, 3, 6, 10, ___?

(a) 12     (b) 14     (c) 15     (d) 16

2.     Which of these is a square number?

(a) 15     (b) 21     (c) 36     (d) 40

3.     In the doubling pattern 1, 2, 4, 8, 16, what is the 7th term?

(a) 32     (b) 64     (c) 128     (d) 96

4.     In the Virahanka numbers 1, 1, 2, 3, 5, 8, 13, which rule connects one term to the next?

(a) Multiply the term by 2     (b) Add the two previous terms     (c) Add 3 each time     (d) Subtract 1 each time

5.     A position-to-term rule is more useful than a term-to-term rule mainly because it:

(a) Uses smaller numbers     (b) Lets us find any term directly, without finding every earlier term     (c) Only works for shapes     (d) Cannot be used for square numbers

6.     What is the 4th cube number?

(a) 16     (b) 24     (c) 64     (d) 81

7.     Along which diagonal of Pascal's Triangle do the triangular numbers appear?

(a) The outer edge of 1s     (b) The second diagonal (counting numbers)     (c) The third diagonal     (d) They do not appear in Pascal's Triangle

B. Fill in the Blanks (1 mark each)

1.     A pattern is an arrangement that follows a fixed _____________.

2.     The sequence 1, 4, 9, 16 is known as the _____________ numbers.

3.     Triangular numbers are formed by adding one _____________ than the previous time.

4.     The Virahanka numbers are also widely known, outside India, as the _____________ sequence.

5.     The four steps of the pattern-thinking process are Observe, Identify, Predict, and _____________.

6.     A square number can be rebuilt as the sum of consecutive _____________ numbers, called gnomons.

7.     The ratio of consecutive Virahanka numbers slowly approaches a value known as the _____________ ratio.

C. Short Answer Questions (2 marks each)

1.     Define a pattern in your own words and give one example from daily life that is not mentioned in this chapter.

2.     What is the difference between a term-to-term rule and a position-to-term rule? Give one example of each.

3.     Write the first five terms of the square numbers and explain how each term is formed.

4.     Explain, using the chessboard story, why the doubling pattern can be misleading if we judge it only by its first few terms.

5.     List, in order, the four steps of the pattern-thinking process described in this chapter.

6.     What is a gnomon, and how does it help explain why square numbers grow the way they do?

7.     Name two places, other than a mathematics textbook, where the Virahanka numbers or the golden ratio have been observed.

D. Short Answer Questions (3 marks each)

1.     A pattern begins 2, 5, 10, 17, 26. Find the rule connecting the position of a term to its value, and use it to find the 8th term. Show your reasoning.

2.     Explain, with a labelled diagram or dot arrangement of your own, why adding two consecutive triangular numbers always produces a square number.

3.     A student claims that the pattern-thinking process (Observe, Identify, Predict, Verify) is only useful in mathematics class. Do you agree or disagree? Support your answer with one example from outside mathematics.

4.     Build the first six rows of Pascal's Triangle and identify the triangular numbers hidden along one of its diagonals.

E. Long Answer / Critical Thinking Questions (5 marks each)

1.     A school is arranging chairs for an annual function in a triangular formation: 1 chair in the front row, 2 in the next, 3 in the next, and so on. (a) How many chairs are needed if there are 10 rows in total? (b) If only 200 chairs are available, what is the maximum number of complete rows that can be formed? Show all your working and explain the rule you used at each step.

2.     Compare the doubling pattern and the Virahanka pattern. In your answer, describe how each pattern is formed, how quickly each one grows, and explain, using one real-life example for each, where such a pattern might be observed. Conclude your answer by explaining how recognising these patterns connects to the idea of computational thinking discussed in this chapter.

3.     Design your own growing shape pattern using two different shapes (similar to the hexagon-and-diamond example in Section 1.3). Draw the first three terms, write the number pattern each shape follows, and state both a term-to-term and a position-to-term rule for one of the two shapes.

Last modified: Thursday, 8 October 2026, 5:48 AM