Pattern Analysis:

In order to find the next term in the given sequence, we need to analyze the pattern followed in the sequence.

- The first term of the sequence is 2.
- The second term is obtained by multiplying the first term with 3 and adding 0. The second term is 6 = (2 × 3) + 0.
- The third term is obtained by multiplying the second term with 5 and adding 5. The third term is 25 = (6 × 5) + 5.
- The fourth term is obtained by multiplying the third term with 4 and subtracting 4. The fourth term is 96 = (25 × 4) − 4.
- The fifth term is obtained by multiplying the fourth term with 3 and subtracting 3. The fifth term is 285 = (96 × 3) − 3.
- The sixth term is obtained by multiplying the fifth term with 2 and subtracting 2. The sixth term is 568 = (285 × 2) − 2.

From the above analysis, we can see that the pattern followed in the sequence is:
- Multiply the previous term with a number and add or subtract another number to get the next term.

Using this pattern, we can find the next term in the sequence.

Solution:

The sixth term of the sequence is 568. To find the seventh term, we need to multiply 568 with 1 and add 1 to it. Therefore, the seventh term of the sequence is:

7th term = (568 × 1) + 1
= 569

Therefore, the next term in the sequence is 569.

Answer:

The next term in the sequence is option (c) 566.