Which number will replace the question mark (?) in the following series?

3, 4, 5, 6, 9, 10, 11, 12, 15, ?

16

The correct answer is Option (1) → 16

1. Identify the Groups

If we look closely at the numbers, the series appears to be organized into sets of four consecutive numbers, with a "jump" between each set.

• Group 1: 3, 4, 5, 6 (Consecutive numbers)
• Jump: 6 to 9 (Difference of +3)
• Group 2: 9, 10, 11, 12 (Consecutive numbers)
• Jump: 12 to 15 (Difference of +3)
• Group 3: 15, ?

2. Determine the Next Number

Since the series has just started a new group of consecutive numbers with 15, the next number in the sequence should simply be the next consecutive integer.

$15 + 1 = 16$

3. Alternative View (Arithmetic Pattern)

You can also see the pattern as a repeating sequence of differences:

• 3 (+1) $\rightarrow$ 4
• 4 (+1) $\rightarrow$ 5
• 5 (+1) $\rightarrow$ 6
• 6 (+3) $\rightarrow$ 9
• 9 (+1) $\rightarrow$ 10
• 10 (+1) $\rightarrow$ 11
• 11 (+1) $\rightarrow$ 12
• 12 (+3) $\rightarrow$ 15
• 15 (+1) $\rightarrow$ 16

The pattern of additions is: +1, +1, +1, +3, repeating. After 15, the pattern resets to +1.

Final Answer: The missing number is 16.