he sequence, $$ \left(\frac{4}{3}\right)^{2},\left(\frac{7}{3}\right)^{2},\left(\frac{10}{3}\right)^{2} $$

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We begin by writing the terms of the sequence:

- $$ a_1 = \left(\frac{4}{3}\right)^2 $$
- $$ a_2 = \left(\frac{7}{3}\right)^2 $$
- $$ a_3 = \left(\frac{10}{3}\right)^2 $$

Notice that the numerators (4, 7, 10) form an arithmetic sequence where each term increases by 3. In other words, the first term is 4 and each subsequent term is given by
$$
4,\, 4+3,\, 4+2\cdot3,\, \ldots
$$
Thus, the general expression for the numerator of the $$ n $$-th term is
$$
3n + 1 \quad \text{(since for $$ n=1 $$: $$ 3\cdot1+1=4 $$, for $$ n=2 $$: $$ 3\cdot2+1=7 $$, and so on)}.
$$

Since the sequence involves squaring each term of the form $$\frac{\text{numerator}}{3}$$, the general $$ n $$-th term of the sequence is:
$$
a_n = \left(\frac{3n+1}{3}\right)^2.
$$

We can also expand and simplify this expression:
$$
a_n = \frac{(3n+1)^2}{9}.
$$

This is the formula for the $$ n $$-th term of the sequence.
The $$ n $$-th term of the sequence is $$ a_n = \left(\frac{3n+1}{3}\right)^2 $$ or $$ a_n = \frac{(3n+1)^2}{9} $$.

he sequence,

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