Page 28 - Ganit Kaushal

Exercise 1.3

1. Which number sequence does the number of vertices in the shape sequence of regular polygons follow?
Give its significance.

2. Which number sequence is obtained by counting the small squares in each shape of the sequence of
stacked squares?
3. Which number sequence is obtained by counting the small triangles in each shape of the sequence of
stacked triangles and why? (Hint: See Ex 3, section 1.8)
4. Which number sequence do you get by counting the number of lines in the shape sequence of complete
graphs? Explain the pattern.
5. In the process of making Koch snowflakes, with each iteration, the perimeter of the snowflake

(a) increases (b) decreases (c) remains constant (d) none of these
6. In the process of making Koch snowflakes, we start with a/an
(a) rhombus (b) isosceles triangle (c) equilateral triangle (d) square

7. Observe the pattern in the five-rowed conical figure given below and answer the following questions.
First Row: Sequence: 1 4 10 35

Second Row: First difference: 3 6 15

Third Row: Second difference: 3 5

Fourth Row: Third difference: 1 1

Fifth Row: _____________ 0
(a) Recognise the pattern of the sequence in the first row and fill in the boxes there.
(b) Recognise the pattern of the sequence in the second row and fill in the boxes there.

(c) Recognise the pattern of the sequence in the third row and fill in the boxes there.
(d) Recognise the pattern of the sequence in the fourth row and fill in the boxes there.
(e) Fill in the blanks and boxes in the fifth row.

Miscellaneous Solved Examples

There are four options (Q. 1 to Q. 2) out of which only one is correct. Choose the correct option.

Ex 1. Observe the pattern of letters in the sequence given below and choose the correct option to fill in the
blanks.
a ___ bc ___ a ___ caa ___ c ___ ab ___
(a) acccbc (b) cbbaca (c) aabbac (d) abbbac

Sol. (c) [ it has a repeated pattern of ‘aabc’]
Ex 2. Which of the following is not a member of the square number pattern?
(a) 100 (b) 121 (c) 144 (d) 159

Sol. (d) [ 159 is not a square of any natural number]

26 Mathematics-6