First five terms?

a(1) = 7, a(n) = a(n - 1) - 3 for n ≥ 2

Explanation:

The notation a(1) = 7 means that the first term is 7

The second term would be a(2) and so on.

To get a(2), we plug in n = 2 to find that...

a(n) = a(n-1) - 3

a(2) = a(2-1) - 3

a(2) = a(1) - 3

a(2) = 7 - 3

a(2) = 4

The second term is 4. We find this by subtracting 3 from the first term.

To get the third term, we repeat the same set of steps but now use n = 3

a(n) = a(n-1) - 3

a(3) = a(3-1) - 3

a(3) = a(2) - 3

a(3) = 4 - 3

a(3) = 1

This process is repeated as much as you want to generate as many terms as you want.

In short, you subtract 3 from each term to get the next term. This implies that we have an arithmetic sequence with starting term 7 and common difference -3.

So that's how we end up with the first five terms: 7, 4, 1, -2, -5