NCERT Solutions Class 6 Maths Chapter 3 — Patterns in Mathematics

Solution:

Step 1: Let's find the difference between consecutive numbers:

Step 2: 7 - 3 = 4

Step 3: 11 - 7 = 4

Step 4: 15 - 11 = 4

Step 5: Since the difference is consistently 4, the rule is to add 4 to the previous number.

Solution:

Step 1: Let's look at the relationship between consecutive terms:

Step 2: 6 ÷ 2 = 3

Step 3: 18 ÷ 6 = 3

Step 4: 54 ÷ 18 = 3

Step 5: The pattern is to multiply the previous number by 3. So, the next number will be 54 × 3 = 162.

Solution:

Step 1: Figure 1 has 1 square (1 × 1).

Step 2: Figure 2 has 4 squares (2 × 2).

Step 3: Figure 3 has 9 squares (3 × 3).

Step 4: The number of squares is the figure number multiplied by itself (the square of the figure number). For the fourth figure, it will be 4 × 4 = 16 squares.

Solution:

Step 1: A) Sum of two odd numbers: 3 + 5 = 8 (Even). So, A is false.

Step 2: B) Product of an odd and an even number: 3 × 4 = 12 (Even). So, B is false.

Step 3: C) Product of two odd numbers: 3 × 5 = 15 (Odd). This statement is always true.

Step 4: D) Sum of two even numbers: 2 + 4 = 6 (Even). So, D is false.

Solution:

Step 1: Let's check Ravi's rule: If the rule is 'multiply by 2', then 10 × 2 = 20 (correct for the first step). But for the next step, 20 × 2 = 40, which is not 30. So, Ravi is incorrect.

Step 2: Let's find the actual difference: 20 - 10 = 10, 30 - 20 = 10, 40 - 30 = 10.

Step 3: The pattern is to add 10 to the previous number.