Question

Consider the first four terms of an arithmetic sequence below.

Answer 1

7, 13, 19 and 25 have a common difference:  6.  
6 added to 7 gives us 13; 6 added to 13 gives us 19, and so on.

Explicit formula:  a(n) = 7 + 6(n-1), where 7 is the first term and n is the counter (1, 2, 3, ...).

The first term is 7 (given).  This corresponds to n=1.

The second term is a(2) = 7 + 6(2-1), or 7 + 6, or 13.  This corresponds to n = 2.

and so on.