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Chapter 1: Patterns in Mathematics 11. Sequence of hexagonal numbers; Yes
Pictorial representation of each hexagonal
Exercise 1.1 number (see figure) shows that it is made
up of six dot triangles plus a dot at the
1. 16 : 25 : 2. 8 : 20 : centre. In the figure we have shown the
fourth hexagonal number with 37 dots, being divided
3. 15 : into six triangles plus one dot at the centre.
12. (a) 15 (b) 22
4. (a) 999999999991 (b) 99999999999991 (c) If the number of triangles formed is ‘n’, then the
5. (a) 1 + 3 + 5 + 7 (b) 1 + 3 + 5 + 7 + 9 number of matchsticks required = 2n + 1.
(c) 1 + 3 + 5 + 7 + 9 + 11. 13. (a) 38 (b) 15
6. (d) ( it follows the repeated pattern ‘daad’.) (c) If the number of A’s formed is ‘n’, then the number
7. (d) ( the repeated pattern is ‘abb’) of matchsticks required = 4n + 2.
8. 2999997 9. 111110888889 Exercise 1.3

10. (a) 80, 160, 320 1. Sequence of counting numbers starting from 3. i.e., 3,
4, 5, 6, 7, …..
2
2
(b) 225, 256 ( 15 = 225, 16 = 256) (c) 87, 81 2. The sequence of squares, that is, 1, 4, 9, 16, 25 and so

11. 3, 5, 9, 17, 33, 65, 129 12. `40 13. 256 on.

14. 12345 × 8 + 5 = 98765; 123456 × 8 + 6 = 987654; 3. The sequence of squares, that is, 1, 4, 9, 16, 25 and so

1234567 × 8 + 7 = 9876543; 12345678 × 8 + 8 = on.
98765432 4. The sequence of triangular numbers, i.e., 1, 3, 6, 10,

Exercise 1.2 15 and so on.
1. (a) 15; (b) 20; 5. (a) 6. (c)
7. (a) Adding up the triangular numbers we get tetrahedral
(c) 21; number; 20, 56.
(b) The sequence of triangular numbers starts from
2. 8th triangular number is 36, which is also a square three; 10, 21.

number. (c) The sequence of counting numbers starts from three;
2
3. (100) = 10000 4, 6.

4. Sequence of Counting Numbers, Sequence of odd (d) All 1’s constant sequence; 1.
numbers. (e) Fourth difference; 0
5. Sequence of triangular numbers. Miscellaneous Exercise 1.4 3. (d) 4. (b)
1.
2. (d)
(b)
6
1442443 = (1 + 2 + 3 + 4 + 5 + 6) 5. (a) 45 (b) True (b) Triangular numbers

5+
4+
(c) Growing/Increasing
(e) 64, 8, 4
(d) 48
3+
(d) True
6.
(a) True
(c) False
2+
6. Square Sequence. 1+ (e) True
th
th

7. 8 term of triangular sequence coincides with 6 term 7. (a) 3021 (b) 4216 (c) 7224 (d) 5609
of a square sequence; 36. 8. 13 (Hint: 6th term of Virahānka sequence)

8. Because they can be represented by a triangular figure Assertion Reason Type Questions
formed by dots. 1. (a) 2. (b) 3. (c) 4. (d)

9. Because they can be represented by a square formed 5. (c) 6. (b) 7. (a) 8. (d)
by dots. Chapter Test
10. Because they can be represented by cubes made up of I. 1. (c) 2. (b) 3. (d) 4. (c)

smaller cubes of unit side. 5. (a)
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