Grade 6 : Mathematics (Ganita Prakash) - Patterns in Mathematics (Set 1) | Concept of Maths

Question 1

1. Consider the numerical sequence: $7, 12, 17, 22, \dots$. What is the $10^{th}$ term of this pattern?

A) 47

B) 52

C) 57

D) 62

Answer

Correct Answer: B

Solution: The sequence starts at $7$ and increases by $5$ each time. Rule: $n^{th}$ term $= 7 + (n-1) \times 5$ For $n = 10$: $7 + (10-1) \times 5 = 7 + 9 \times 5 = 7 + 45 = 52$.

Question 2

2. A student uses matchsticks to form the letter 'V'. To make one 'V', 2 sticks are needed. To make two 'V's, 4 sticks are needed. What is the general rule for the number of sticks required to make $n$ such 'V's?

A) $n + 1$

B) $2n$

C) $3n - 1$

D) $n^2$

Answer

Correct Answer: B

Solution: 1 'V' = $2$ sticks 2 'V's = $4$ sticks 3 'V's = $6$ sticks The number of sticks is twice the number of letters. Thus, the rule is $2 \times n$ or $2n$.

Question 3

3. Observe the pattern of sums of consecutive odd numbers: $1 = 1^2$ $1 + 3 = 2^2$ $1 + 3 + 5 = 3^2$ Based on this pattern, what is the sum of the first 4 odd numbers ($1 + 3 + 5 + 7$)?

A) 12

B) 14

C) 16

D) 18

Answer

Correct Answer: C

Solution: The pattern shows that the sum of the first $n$ odd numbers is $n^2$. For the first 4 odd numbers, the sum is $4^2 = 4 \times 4 = 16$.

Question 4

4. Find the missing term in the geometric sequence: $3, 9, 27, 81, \dots$

Question 5

5. Look at the sequence of triangular dots: $1, 3, 6, 10, \dots$. What is the next number in this sequence?

A) 13

B) 14

C) 15

D) 16

Answer

Correct Answer: C

Solution: This is the sequence of triangular numbers. The difference between terms increases by 1 each time: $3 - 1 = 2$ $6 - 3 = 3$ $10 - 6 = 4$ The next difference should be $5$. So, $10 + 5 = 15$.

Question 6

6. If a pattern follows the algebraic rule $4n - 1$, where $n$ is the position of the term, what is the value of the $10^{th}$ term?

A) 39

B) 40

C) 41

D) 42

Answer

Correct Answer: A

Solution: Substitute $n = 10$ into the expression $4n - 1$: Value $= 4(10) - 1 = 40 - 1 = 39$.

Question 7

7. Observe the multiplication pattern: $11 \times 11 = 121$ $111 \times 111 = 12321$ What is the result of $1111 \times 1111$ according to this pattern?

A) 123321

B) 1234321

C) 123454321

D) 124321

Answer

Correct Answer: B

Solution: The pattern shows that the product of a number consisting only of $n$ ones with itself results in a palindrome that counts up to $n$ and back to $1$. For $1111$ (four ones), the result is $1234321$.

Question 8

8. A pattern of squares is made using matchsticks. 1 square needs 4 sticks, 2 connected squares need 7 sticks, 3 connected squares need 10 sticks. How many sticks are needed for 20 such connected squares?

A) 60

B) 61

C) 63

D) 80

Answer

Correct Answer: B

Solution: The pattern is: $4, 7, 10, \dots$ The rule for $n$ squares is $3n + 1$. For $n = 20$: $3 \times 20 + 1 = 60 + 1 = 61$ sticks.

Question 9

9. Identify the next term in the decreasing sequence: $100, 91, 82, 73, \dots$

A) 65

B) 64

C) 63

D) 62

Answer

Correct Answer: B

Solution: Calculate the difference between consecutive terms: $100 - 91 = 9$ $91 - 82 = 9$ $82 - 73 = 9$ The sequence decreases by $9$ each time. The next term is $73 - 9 = 64$.

Question 10

10. In a geometry pattern, if the side length of an equilateral triangle is denoted by $s$, which algebraic expression represents its perimeter?

A) $s^2$

B) $2s$

C) $3s$

D) $4s$

Answer

Correct Answer: C

Solution: The perimeter of a shape is the total length of its boundary. An equilateral triangle has 3 sides of equal length $s$. Perimeter $= s + s + s = 3 \times s = 3s$.

Accepted Answer

Correct Answer: B

Solution: Each term is obtained by multiplying the previous term by $3$. $3 \times 3 = 9$ $9 \times 3 = 27$ $27 \times 3 = 81$ $81 \times 3 = 243$.

Grade 6 : Mathematics (Ganita Prakash) - Patterns in Mathematics (Set 1) | Concept of Maths