Which number will replace the question mark (?) in the following series?
3, 4, 5, 6, 9, 10, 11, 12, 15, ?
Answer & explanation
Correct answer: option 1
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.