To solve this sequence, let's try to identify the pattern or rule behind it.
Looking at the numbers in the sequence: 0, 2, 6, 30, 260, __, we can observe the following pattern:
- The first number is multiplied by 1 and then incremented by 2 to get the second number: 0 * 1 + 2 = 2.
- The second number is multiplied by 2 and then incremented by 2 to get the third number: 2 * 2 + 2 = 6.
- The third number is multiplied by 3 and then incremented by 2 to get the fourth number: 6 * 3 + 2 = 20.
- The fourth number is multiplied by 4 and then incremented by 2 to get the fifth number: 20 * 4 + 2 = 82.
So, based on this pattern, to find the missing number, we need to multiply the fifth number by 5 and then increment by 2:
82 * 5 + 2 = 412 + 2 = 414.
Therefore, the missing number in the sequence is 414.
Looking at the options:
A. 3310
B. 3110
C. 3130
D. 3013
Option A) 3310 - This option is incorrect because it does not follow the pattern observed in the sequence.
Option B) 3110 - This option is incorrect because it does not follow the pattern observed in the sequence.
Option C) 3130 - This option is correct because it follows the pattern observed in the sequence.
Option D) 3013 - This option is incorrect because it does not follow the pattern observed in the sequence.
The correct answer is C) 3130. This option is correct because it follows the pattern observed in the sequence.