Let's denote the first term of the arithmetic progression (A.P.) as \(a\), and the common difference as \(d\).

The formula for the \(n\)th term of an arithmetic progression is given by:

\(a_n = a + (n-1)d\)

Given that the sixth term of the A.P. is half of its twelfth term, we can write this as:

\(a + 5d = \frac{1}{2} \cdot (a + 11d)\)

Simplify the equation:

\(2(a + 5d) = a + 11d\)

\(2a + 10d = a + 11d\)

Subtracting \(a\) and \(10d\) from both sides:

\(a = d\)

So, the first term of the A.P. is equal to the common difference.