To identify the pattern in the given sequence, let's look at the differences between consecutive terms:
1st difference: 2 - 0 = 2
2nd difference: 6 - 2 = 4
3rd difference: 30 - 6 = 24
4th difference: 260 - 30 = 230
The differences between consecutive terms are not consistent. Therefore, we need to consider an alternative approach.
Let's try multiplying each term by a specific value to see if there is a pattern:
0 * 1 = 0
2 * 3 = 6
6 * 5 = 30
30 * 9 = 270
260 * 11 = 2860
Now, let's examine the second differences:
1st difference: 6 - 0 = 6
2nd difference: 30 - 6 = 24
3rd difference: 270 - 30 = 240
4th difference: 2860 - 270 = 2590
The second differences are not consistent either. However, we can observe that the values obtained by multiplying each term by a specific value are close to the corresponding terms in the given sequence.
Therefore, the next term in the sequence can be obtained by multiplying 260 by a specific value:
260 * 12 = 3120
Among the given options, the closest value to 3120 is option D) 3130.
Therefore, the correct answer is D) 3130.