Fill in the blanks in the following table,given that $a$ is the first term,$d$ is the common difference,and $a_{n}$ is the $n^{th}$ term of the $AP$:
$S.No.$$a$$d$$n$$a_{n}$
$(i)$$7$$3$$8$$...$
$(ii)$$-18$$...$$10$$0$
$(iii)$$...$$-3$$18$$-5$
$(iv)$$-18.9$$2.5$$...$$3.6$
$(v)$$3.5$$0$$105$$...$

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(N/A) The general term of an $AP$ is given by the formula: $a_{n} = a + (n - 1)d$.
$(i)$ Given $a = 7, d = 3, n = 8$.
$a_{8} = 7 + (8 - 1)3 = 7 + (7)(3) = 7 + 21 = 28$.
$(ii)$ Given $a = -18, n = 10, a_{n} = 0$.
$0 = -18 + (10 - 1)d \rightarrow 18 = 9d \rightarrow d = 2$.
$(iii)$ Given $d = -3, n = 18, a_{n} = -5$.
$-5 = a + (18 - 1)(-3) \rightarrow -5 = a + (17)(-3) \rightarrow -5 = a - 51 \rightarrow a = 46$.
$(iv)$ Given $a = -18.9, d = 2.5, a_{n} = 3.6$.
$3.6 = -18.9 + (n - 1)2.5 \rightarrow 3.6 + 18.9 = (n - 1)2.5 \rightarrow 22.5 = (n - 1)2.5 \rightarrow n - 1 = 9 \rightarrow n = 10$.
$(v)$ Given $a = 3.5, d = 0, n = 105$.
$a_{105} = 3.5 + (105 - 1)0 = 3.5 + 0 = 3.5$.

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