If the sum of the first $n$ terms of an $AP$ is $4n - n^2$,what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly,find the $3^{rd}$,the $10^{th}$ and the $n^{th}$ terms.

(N/A) Given that,the sum of the first $n$ terms is $S_n = 4n - n^2$.
$1$. The first term $(a_1)$ is equal to $S_1$:
$a_1 = S_1 = 4(1) - (1)^2 = 4 - 1 = 3$.
$2$. The sum of the first two terms is $S_2$:
$S_2 = 4(2) - (2)^2 = 8 - 4 = 4$.
$3$. The second term $(a_2)$ is $S_2 - S_1$:
$a_2 = 4 - 3 = 1$.
$4$. The common difference $(d)$ is $a_2 - a_1 = 1 - 3 = -2$.
$5$. The $n^{th}$ term $(a_n)$ is given by $a + (n - 1)d$:
$a_n = 3 + (n - 1)(-2) = 3 - 2n + 2 = 5 - 2n$.
$6$. Finding specific terms:
$a_3 = 5 - 2(3) = 5 - 6 = -1$.
$a_{10} = 5 - 2(10) = 5 - 20 = -15$.
Thus,the first term is $3$,the sum of the first two terms is $4$,the second term is $1$,the $3^{rd}$ term is $-1$,the $10^{th}$ term is $-15$,and the $n^{th}$ term is $5 - 2n$.