Rule detection is the ability to identify the underlying pattern, rule, or relationship that governs a sequence, set of numbers, letters, shapes, or other data, and then use that rule to predict or determine the next element.
Rule Detection - Solved Examples
Example 1: Scenario: In the sequence 1, 2, 5, 6, 7, 10, 11, 12, ?, every third number is a multiple of 5. What is the next multiple of 5?
What is the next multiple of 5 in the sequence?
a) 10
b) 12
c) 15
d) 18
Answer: c) 15
Explanation: The rule is that every third number is a multiple of 5. So, starting from 5, the sequence would be 5, 10, 15, 20, and so on. The next multiple of 5 is 15.
Example 2: Scenario: In a pattern, you observe the sequence: 2, 4, 8, 16, ___.
What is the next number?
a) 24
b) 32
c) 48
d) 64
Answer: d) 32
Explanation: The rule is that each number is doubled to get the next number. So, 16 doubled is 32
Example 3: Scenario: In a sequence of letters, you notice the pattern: A, C, E, G, ___.
What letter comes next?
a) H
b) I
c) F
d) J
Answer: c) I
Explanation: Assuming the sequence starts with the first letter of the alphabet (A), the next letter would be I. This pattern skips every other letter in the alphabet.
Example 4: Scenario: In a sequence of numbers, you notice that every even number is followed by the next odd number.
What comes after 10?
a) 9
b) 11
c) 12
d) 8
Answer: b) 11
Explanation: The rule is that every even number is followed by the next odd number. So, after 10 (an even number), the next number is 11 (the next odd number).
Example 5: Scenario: In a sequence, you observe that each term is obtained by adding 3 to the previous term.
If the sequence starts with 5, what is the fifth term?
a) 11
b) 12
c) 13
d) 17
Answer: c) 17
Explanation: ince each term is obtained by adding 3 to the previous term, we can use the formula for the nth term of an arithmetic sequence to find the fifth term. The formula for the nth term of an arithmetic sequence is: a_n = a_1 + d(n - 1) and the solution is 17
Example 6: Scenario: In the following sequence, every odd-positioned term is a prime number.
What is the next prime number in the sequence: 2, 6, 3, 9, ___
a) 12
b) 5
c) 15
d) 11
Answer: b) 11
Explanation: The rule is that every other number is a prime number. In the given sequence, 2 and 3 are prime numbers, so the next prime number is 11.
Example 7: Scenario: In a sequence, you notice the pattern: 1, 4, 9, 16, ___.
What is the next number?
a) 20
b) 24
c) 25
d) 28
Answer: c) 25
Explanation: The rule is that each number is a perfect square of consecutive positive integers. 1 is 1^2, 4 is 2^2, 9 is 3^2, 16 is 4^2. The next perfect square is 5^2, which is 25.
Example 8: Scenario: In a sequence of letters, you observe the pattern: B, E, H, K, ___.
What letter comes next?
a) M
b) L
c) N
d) O
Answer: c) N
Explanation: The rule is that each letter is followed by the next letter in the alphabet with an increment of 3. So, B is followed by E, E is followed by H, H is followed by K, and the next letter is K + 3, which is N.
Example 9: Scenario: You notice a pattern where the numbers are increasing by 5, then decreasing by 3.
If the sequence starts with 10, what is the next number? 10, 15, 12, ___
a) 12
b) 15
c) 17
d) 18
Answer: c) 17
Explanation: The rule is that the numbers increase by 5, then decrease by 3. Starting with 10, the sequence would be 10, 15 (increased by 5), 12 (decreased by 3), and the next number is 12 + 5 = 17 (increased by 5).
Example 10: Scenario: In a sequence of shapes, you notice the pattern: Circle, Square, Triangle, Circle, Square, ___.
What shape comes next?
a) Star
b) Oval
c) Rectangle
d) Triangle
Answer: d) Triangle
Explanation: The rule is that the shapes repeat in a cycle: Circle, Square, Triangle. After Triangle, the next shape in the cycle is Circle.
