2,6,30,260...

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.

• Thanks
• Wrong explanation