Copy the pictorial representations of the number sequences in Table 2 in your notebook, and draw the next picture for each sequence!

Question

Homi · Accepted Answer

Understand the Question

To find and draw the next pictorial representation for each number sequence:

Identify the pattern rule: Determine how each term changes from the previous one (e.g., constant, fixed addition, increasing differences, squares, or cubes).
Calculate the next number: Apply the rule to find the 6th term in each sequence.
Draw the visual representation: Arrange dots or unit cubes to match the geometric shape of the pattern.

(i) All 1's

Step 1 · Find the Next Term for All 1's

This sequence remains constant at $1$ dot for every term. Diagram 1

$\text{Next term} = 1$

Answer

(i) $1\text{ dot}$

(ii) Counting numbers

Step 1 · Find the Next Counting Number

The sequence increases by $1$ dot at each step: $1, 2, 3, 4, 5, \dots$ Diagram 2

$\text{Next number} = 5 + 1 = 6$

Answer

(ii) $6\text{ dots}$

(iii) Odd numbers

Step 1 · Find the Next Odd Number

The sequence of odd numbers increases by $2$ dots at each step: $1, 3, 5, 7, 9, \dots$ Diagram 3

$\text{Next number} = 9 + 2 = 11$

Answer

(iii) $11\text{ dots}$

(iv) Even numbers

Step 1 · Find the Next Even Number

The sequence of even numbers increases by $2$ dots at each step: $2, 4, 6, 8, 10, \dots$ Diagram 4

$\text{Next number} = 10 + 2 = 12$

Answer

(iv) $12\text{ dots}$

(v) Triangular numbers

Step 1 · Find the Next Triangular Number

The sequence adds consecutive natural numbers: $+2, +3, +4, +5, \dots$ The given numbers are $1, 3, 6, 10, 15$ . Diagram 5

$\text{Next number} = 15 + 6 = 21$

Answer

(v) $21\text{ dots}$

(vi) Squares

Step 1 · Find the Next Square Number

The sequence shows dots arranged in squares of dimensions $1\times 1, 2\times 2, 3\times 3, 4\times 4, 5\times 5$ . Diagram 6

$\text{Next square} = 6 \times 6 = 36$

Answer

(vi) $36\text{ dots}$

(vii) Cubes

Step 1 · Find the Next Cube Number

The sequence shows 3D cubes formed by unit cubes of dimensions $1^3, 2^3, 3^3, 4^3, 5^3$ . Diagram 7

$\text{Next cube} = 6 \times 6 \times 6 = 216$

Answer

(vii) $216\text{ unit cubes}$

Common Mistakes

Triangular Pattern Error: Adding a constant number rather than an increasing increment ( $+2, +3, +4, +5, +6$ ).
Squares vs. Cubes: Confusing $6^2 = 36$ with $6^3 = 216$ .
Missing Geometric Arrangement: Drawing the correct number of dots randomly instead of matching the specific shape (e.g., triangle, square grid, or 3D cube).

Question 5

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