Question 1

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

A) 47B) 52C) 57D) 62

Answer

✓ Correct Answer: Option B

Explanation: 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 + 1B) 2n 3n - 1

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) 12B) 14C) 16D) 18

Answer

✓ Correct Answer: Option C

Explanation: 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

A) 162B) 243C) 324D) 729

Answer

✓ Correct Answer: Option B

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

Question 5

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

A) 13B) 14C) 15D) 16

Answer

✓ Correct Answer: Option C

Explanation: 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) 39B) 40C) 41D) 42

Answer

✓ Correct Answer: Option A

Explanation: 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) 123321B) 1234321C) 123454321D) 124321

Answer

✓ Correct Answer: Option B

Explanation: 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) 60B) 61C) 63D) 80

Answer

✓ Correct Answer: Option B

Explanation: 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) 65B) 64C) 63D) 62

Answer

✓ Correct Answer: Option B

Explanation: 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) 2sC) 3sD) 4s

Answer

✓ Correct Answer: Option C

Explanation: 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: Option B

Explanation: 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.

Grade 6 : Mathematics (Ganita Prakash) - Patterns in Mathematics (Set 1)

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

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?

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

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

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

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?

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

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?

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

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