To find the pattern in the given sequence: 2, 6, 30, 260...
Let's analyze the differences between consecutive terms:
6 - 2 = 4
30 - 6 = 24
260 - 30 = 230
The differences themselves do not form a clear pattern. However, let's analyze the differences between those differences:
24 - 4 = 20
230 - 24 = 206
The second difference, 206, is not a constant difference. Therefore, the given sequence does not follow a simple arithmetic pattern.
Instead, let's try a different approach. Let's consider the prime factorization of each number in the sequence:
2 = 2^1
6 = 2^1 * 3^1
30 = 2^1 * 3^1 * 5^1
260 = 2^2 * 5^1 * 13^1
From the prime factorization, we can see that the exponent of the prime factors is increasing by 1 for each term in the sequence.
Therefore, the next term in the sequence should have an exponent of 1 for the next prime number, which is 7.
So, the next term in the sequence would be:
7^1 = 7
Hence, the correct answer is C) 3130.