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In an AP:
(i) given \( a=5, d=3, a_{n}=50 \), find \( n \) and \( \mathrm{S}_{n} \).
(ii) given \( a=7, a_{13}=35 \), find \( d \) and \( \mathrm{S}_{13} \).
(iii) given \( a_{12}=37, d=3 \), find \( a \) and \( S_{12} \).
(iv) given \( a_{3}=15, \mathrm{~S}_{10}=125 \), find \( d \) and \( a_{10^{\circ}} \).
(v) given \( d=5, \mathrm{~S}_{9}=75 \), find \( a \) and \( a_{9} \).
(vi) given \( a=2, d=8, \mathrm{~S}_{n}=90 \), find \( n \) and \( a_{n} \).
(vii) given \( a=8, a_{n}=62, \mathrm{~S}_{n}=210 \), find \( n \) and \( d \).
(viii) given \( a_{n}=4, d=2, \mathrm{~S}_{n}=-14 \), find \( n \) and \( a \). .
(ix) given \( a=3, n=8, \mathrm{~S}=192 \), find \( d \).
(x) given \( l=28, \mathrm{~S}=144 \), and there are total 9 terms. Find \( a \).
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