Give a recursive definition of the sequence a_n = 2n for n = 2, 3, 4 where a_1 = 2

The sequence can be defined recursively by specifying the first term and the relationship between successive terms.

Let’s define the sequence {a_n} recursively as follows:

• Base case: a_1 = 2
• Recursive case: a_n = 2 * n for n ≥ 2

Thus, we have:

• a_1 = 2
• a_2 = 2 * 2 = 4
• a_3 = 2 * 3 = 6
• a_4 = 2 * 4 = 8

This gives us the sequence: 2, 4, 6, 8.

The recursive definition allows us to compute any term in the sequence based on its position (n) and the first term. Starting from a_1, we can easily find a_2, a_3, and so on.