Question 3

In an AP:

(i) given $a = 5$, $d = 3$, $a_n = 50$, find $n$ and $S_n$.

(ii) given $a = 7$, $a_{13} = 35$, find $d$ and $S_{13}$.

(iii) given $a_{12} = 37$, $d = 3$, find $a$ and $S_{12}$.

(iv) given $a_3 = 15$, $S_{10} = 125$, find $d$ and $a_{10}$.

(v) given $d = 5$, $S_9 = 75$, find $a$ and $a_9$.

(vi) given $a = 2$, $d = 8$, $S_n = 90$, find $n$ and $a_n$.

(vii) given $a = 8$, $a_n = 62$, $S_n = 210$, find $n$ and $d$.

(viii) given $a_n = 4$, $d = 2$, $S_n = -14$, find $n$ and $a$.

(ix) given $a = 3$, $n = 8$, $S_n = 192$, find $d$.

(x) given $l = 28$, $S_n = 144$, and there are total $9$ terms. Find $a$.