PI - Cognitive Assessment Number Series Problems 2 — Questions and Answers
Question 1: What comes next: 3, 6, 12, 24, 48, ___?
- 60
- 72
- 96 (Correct answer)
- 84
Correct answer: 96
Each number is doubled: 3×2=6, 6×2=12, 12×2=24, 24×2=48, 48×2=96.
This is a geometric sequence with a common ratio of 2. Each term is multiplied by 2 to get the next term: 3→6→12→24→48→96. On the PI Cognitive Assessment, geometric sequences are common and can be identified by checking if the ratio between consecutive terms is constant (6/3=2, 12/6=2, 24/12=2, etc.).
Question 2: What comes next: 1, 1, 2, 3, 5, 8, ___?
- 11
- 12
- 13 (Correct answer)
- 10
Correct answer: 13
This is the Fibonacci sequence: each number is the sum of the two preceding numbers. 5+8=13.
The Fibonacci sequence is defined by the recurrence relation: F(n) = F(n-1) + F(n-2). Starting with 1, 1: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13. This is one of the most well-known number patterns and appears frequently on cognitive assessments.
Question 3: What comes next: 100, 81, 64, 49, 36, ___?
- 16
- 20
- 25 (Correct answer)
- 30
Correct answer: 25
These are perfect squares in descending order: 10², 9², 8², 7², 6², 5²=25.
The sequence consists of perfect squares of decreasing integers: 10²=100, 9²=81, 8²=64, 7²=49, 6²=36. The next term is 5²=25. Recognizing perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) is an important skill for the PI Cognitive Assessment's number series problems.
Question 4: What comes next: 2, 6, 18, 54, ___?
- 108
- 162 (Correct answer)
- 72
- 216
Correct answer: 162
Each number is multiplied by 3: 2×3=6, 6×3=18, 18×3=54, 54×3=162.
This is a geometric sequence with common ratio 3. Each term is tripled: 2→6→18→54→162. To verify: 6÷2=3, 18÷6=3, 54÷18=3. Therefore 54×3=162. Be careful not to confuse with 54×2=108, which would indicate a ratio of 2.
Question 5: What comes next: 5, 10, 8, 16, 14, 28, ___?
- 24
- 26 (Correct answer)
- 30
- 56
Correct answer: 26
The pattern alternates: ×2, then −2. 5×2=10, 10−2=8, 8×2=16, 16−2=14, 14×2=28, 28−2=26.
This series uses two alternating operations: multiply by 2, then subtract 2. Step by step: 5×2=10, 10−2=8, 8×2=16, 16−2=14, 14×2=28. The next step is subtraction: 28−2=26. Alternating-operation series are challenging because you must identify two different rules and their pattern of application.
Question 6: What comes next: 1, 4, 9, 16, 25, 36, ___?
- 42
- 48
- 49 (Correct answer)
- 64
Correct answer: 49
These are consecutive perfect squares: 1², 2², 3², 4², 5², 6², 7²=49.
The sequence lists perfect squares of consecutive positive integers: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49. The differences between consecutive terms increase by 2 each time (3, 5, 7, 9, 11, 13), which is another way to identify a sequence of perfect squares.
PI - Cognitive Assessment Number Series Problems 2
What comes next: 3, 6, 12, 24, 48, ___?