In a sequence, each term is obtained by adding the same number from the previous term. The first four terms in a sequence are 36, p, q, 93.

1. Find the common difference of the arithmetic sequence.

There are 3 equal intervals from the 1st term to the 4th term:

$36,\ p,\ q,\ 93$

So the common difference is

$\frac{93-36}{3}=\frac{57}{3}=19.$

2. Use the common difference to find p and q.

$p=36+19=55$

$q=55+19=74$

1. Substitute the first term and common difference into the arithmetic sequence formula and simplify.

Since the first term is $36$ and the common difference is $55-36=19$,
$T_n=36+(n-1)(19)$
$T_n=36+19n-19=19n+17$

1. Set the nth term expression equal to 225.

From part (b), $T_n=19n+17$.

If $225$ is a term, then
$19n+17=225.$

2. Solve for n and interpret whether it can be a term number.

$19n=225-17=208$
$n=\frac{208}{19}$

Since $\frac{208}{19}$ is not a positive integer, there is no whole-number term number $n$ for which $T_n=225$.