To find the $n^{th}$ term and the three terms of the arithmetic sequence, we first need to determine the common difference ($d$) and the first term ($a_1$). Given: $a_4 = 93$ $a_8 = 65$ Step 1: Find the common difference ($d$). In an arithmetic sequence, the $n^{th}$ term can be expressed as $a_n = a_k + (n-k)d$. Using $a_8$ and $a_4$: $$a_8 = a_4 + (8-4)d$$ $$a_8 = a_4 + 4d$$ Substitute the given values: $$65 = 93 + 4d$$ Subtract 93 from both sides: $$65 - 93 = 4d$$ $$-28 = 4d$$ Divide by 4: $$d = \frac{-28}{4}$$ $$d = -7$$ Step 2: Find the first term ($a_1$). The general formula for the $n^{th}$ term of an arithmetic sequence is $a_n = a_1 + (n-1)d$. Using $a_4 = 93$ and $d = -7$: $$a_4 = a_1 + (4-1)d$$ $$93 = a_1 + 3(-7)$$ $$93 = a_1 - 21$$ Add 21 to both sides: $$a_1 = 93 + 21$$ $$a_1 = 114$$ Step 3: Find the $n^{th}$ term ($a_n$). Using the general formula $a_n = a_1 + (n-1)d$ with $a_1 = 114$ and $d = -7$: $$a_n = 114 + (n-1)(-7)$$ $$a_n = 114 - 7n + 7$$ $$a_n = 121 - 7n$$ Step 4: Find the first three terms of the sequence. The first term is $a_1 = 114$. The second term is $a_2 = a_1 + d = 114 + (-7) = 107$. The third term is $a_3 = a_2 + d = 107 + (-7) = 100$. The $n^{th}$ term of the arithmetic sequence is $\boxed{\text{121 - 7n}}$. The first three terms of the sequence are $\boxed{\text{114, 107, 100}}$.