Explanation:

Let’s analyze the sequence step by step:

- The series is: 245, 250, 257, 267, 282, 306, 337

- Find the pattern in differences:

- 250 - 245 = 5

- 257 - 250 = 7

- 267 - 257 = 10

- 282 - 267 = 15

- 306 - 282 = 24

- 337 - 306 = 31

- Now, observe the pattern in these differences: 5, 7, 10, 15, 24, 31

- Further differences:

- 7 - 5 = 2

- 10 - 7 = 3

- 15 - 10 = 5

- 24 - 15 = 9

- 31 - 24 = 7

- These are not forming a simple sequence.

- Now, check if 306 fits:

- 282 + ? = 306 ? difference is 24

- Next difference is 31 (to get 337)

- If the series should maintain a pattern, check with nearby numbers. If we follow the previous increments:

- 5, 7 (+2), 10 (+3), 15 (+5), next should be +9 (i.e., 15+9=24), which matches.

- But following that, 24+7=31, which checks out.

So, the pattern is irregulary led by prime sequences (2,3,5,7,9). The only odd jump is from 15 to 24 (should be +7, not +9), so 306 seems correct as per this pattern.

Let's verify if some other number disrupts the pattern:

- If we try 267: 257 + 10 = 267 (This is OK)

- All other numbers fit the emerging pattern.

Hence, the series is correct. THERE IS NO WRONG NUMBER. BUT, with the given choices, everything fits. If forced, the typical sequence alternates after 15 with +7 instead of +9, making 282+7=289, so the next should be 289+15=304, not 306. So 306 is the odd-man out.

Here are the options analyzed:

- 245: First term, likely not wrong.

- 250: Second term, difference is 5.

- 267: Mid-term, fits.

- 306: The jump occurs here, little off if following standard increase.

- 337: Last term, fits as per pattern.

Option 3 (306) is the most likely wrong number.