What will come in place of question mark in following number series ? 6 9 23 87 429

Options

A. 8
B. 4
C. 2
D. 3

Answer

To find the missing number in the series 6, 9, 23, 87, 429, we need to identify the pattern in the sequence. Let's analyze the numbers step by step.

1. **Identify the first two numbers**:
- The first number is 6 and the second number is 9.
- To get from 6 to 9, we can observe that \( 6 \times 1.5 = 9 \).

2. **Identify the next number**:
- The third number is 23.
- To get from 9 to 23, we can try multiplying 9 by a number and then adjusting it.
- If we multiply 9 by 3 and subtract 4, we get \( 9 \times 3 - 4 = 27 - 4 = 23 \).

3. **Continue the pattern**:
- The fourth number is 87.
- To get from 23 to 87, we can multiply 23 by 4 and then subtract 5.
- So, \( 23 \times 4 - 5 = 92 - 5 = 87 \).

4. **Find the next number**:
- The fifth number is 429.
- To get from 87 to 429, we can multiply 87 by 5 and then subtract 6.
- Thus, \( 87 \times 5 - 6 = 435 - 6 = 429 \).

5. **Establish the pattern**:
- The pattern we see is that we multiply by an increasing integer (1, 3, 4, 5) and subtract an increasing integer (2, 4, 5, 6).
- The first number (6) can be derived by multiplying by 1 and subtracting 2: \( 6 \times 1 - 2 = 6 \).

6. **Determine the missing number**:
- To find the missing number, we can work backwards from the second number (9).
- We know that \( 6 \times 1 + 2 = 8 \).
- Therefore, the missing number in the series is 8.

Thus, the missing number in the series is **8**.