To find the pattern in the given sequence, let's examine the differences between consecutive terms:
9 - 5 = 4
25 - 9 = 16
91 - 25 = 66
414 - 91 = 323
We can observe that the differences between consecutive terms are increasing:
4, 16, 66, 323
To continue the pattern, we can add the next difference:
323 + 1 = 324
Now, let's find the next term by adding this difference to the last term in the given sequence:
414 + 324 = 738
Therefore, the next term in the sequence is 738.
Among the given options, the closest value to 738 is option B) 2282.5.
Thus, the correct answer is option B) 2282.5.