Pattern Identification

The problem presents two number sequences where a specific mathematical operation connects consecutive numbers. We need to identify this pattern.

Set 1: 13 - 26 - 30 - 60

• The operation from 13 to 26 is multiplication by 2: \(13 \times 2 = 26\).
• The operation from 26 to 30 is addition of 4: \(26 + 4 = 30\).
• The operation from 30 to 60 is multiplication by 2: \(30 \times 2 = 60\).

The pattern identified is \(\times 2\), \(+ 4\), \(\times 2\).

Set 2: 9 - 18 - 22 - 44

• \(9 \times 2 = 18\) (Matches \(\times 2\))
• \(18 + 4 = 22\) (Matches \(+ 4\))
• \(22 \times 2 = 44\) (Matches \(\times 2\))

The pattern \(\times 2\), \(+ 4\), \(\times 2\) is consistent across both sets.

Option Analysis

We will now check which option follows the identified pattern (\(\times 2\), \(+ 4\), \(\times 2\)):

Option 1: 10 - 20 - 24 - 54

• \(10 \times 2 = 20\)
• \(20 + 4 = 24\)
• \(24 \times 2 = 48\). This is not 54. Option 1 is incorrect.

Option 2: 2 - 4 - 8 - 12

• \(2 \times 2 = 4\)
• \(4 + 4 = 8\)
• \(8 \times 2 = 16\). This is not 12. Option 2 is incorrect.

Option 3: 3 - 6 - 10 - 22

• \(3 \times 2 = 6\)
• \(6 + 4 = 10\)
• \(10 \times 2 = 20\). This is not 22. Option 3 is incorrect.

Option 4: 6 - 12 - 16 - 32

• \(6 \times 2 = 12\)
• \(12 + 4 = 16\)
• \(16 \times 2 = 32\). This matches the pattern. Option 4 is correct.

Final Answer Determination

Option 4 (6 - 12 - 16 - 32) is the only sequence that follows the mathematical operations \(\times 2\), \(+ 4\), \(\times 2\) derived from the given sets.