For the geometric progression (GP), the first term is given as \(a = 192\), the common ratio \(r = 1.5\), and the number of terms \(n = 6\).

The sum of the GP is given by:

\(S_6 = a \frac{r^n - 1}{r - 1} = 192 \frac{1.5^6 - 1}{1.5 - 1}\)

Calculating this gives:

\(S_6 = 192 \times 0.5 \times (1.5^6 - 1) = 3990\)

For the arithmetic progression (AP), the number of terms \(n = 21\), and the common difference \(d = 1.5\).

The sum of the AP is given by:

\(S_{21} = \frac{n}{2} (2a + (n-1)d) = \frac{21}{2} (2a + 20 \times 1.5)\)

Equating the sums of the GP and AP:

\(3990 = \frac{21}{2} (2a + 30)\)

Solving for \(a\):

\(3990 = 21(a + 15)\)

\(3990 = 21a + 315\)

\(21a = 3675\)

\(a = 175\)

The first term of the AP is 175.

The last term of the AP is given by:

\(l = a + 20d = 175 + 20 \times 1.5 = 205\)

Thus, the first term is 175 and the last term is 205.