Find the wrong number in the following number series.
2,3,10,40,172,885,5346

Options

A. A)40
B. B)885
C. C)172
D. D)3

Answer

To find the wrong number in the series 2, 3, 10, 40, 172, 885, 5346, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
Let's look at how each term relates to the previous term:
- From 2 to 3:
- \(2 + 1 = 3\)
- From 3 to 10:
- \(3 + 2 \times 2 = 10\)
- From 10 to 40:
- \(10 + 3 \times 10 = 40\)

### Step 2: Continue the pattern
Now let's check the next terms:
- From 40 to 172:
- We expect \(40 + 4 \times 39\) (but we will check this step later).

Let's calculate what it should be:
- If we follow the pattern, we should have:
- \(40 + 4 \times 39 = 40 + 156 = 196\) (not 172)

### Step 3: Identify the discrepancy
The expected number after 40 should be 196, but the series has 172. This indicates that 40 is likely the wrong number.

### Step 4: Verify the subsequent terms
Now let's check if we can still get the subsequent terms if we replace 40 with 39:
- From 39 to 172:
- \(39 + 4 \times 39 = 39 + 156 = 195\) (not 172)

This confirms that the term 40 is incorrect.

### Step 5: Check the next terms with 39
If we assume the series is:
- 2, 3, 10, 39, 172, 885, 5346
- From 172 to 885:
- \(172 + 5 \times 39 = 172 + 195 = 367\) (not 885)

This also indicates that the pattern is broken.

### Conclusion
The wrong number in the series is 40, and it should be replaced with 39.