Answer
General term($n^{th}$ term) = 2 - $\frac{1}{2}$ n
Indicated term $a_{30}$ = -13
Work Step by Step
The given sequence = $\frac{3}{2}$, 1, $\frac{1}{2}$, 0,..........;$a_{30}$
From above we observe $a_{1}$ = $\frac{3}{2}$
common difference (d) = 0 - $\frac{1}{2}$ = $\frac{1}{2}$ - 1 = 1 - $\frac{3}{2}$ = -$\frac{1}{2}$
General term($n^{th}$ term) = $a_{n}$ = $\frac{3}{2}$ +(n-1)(-$\frac{1}{2}$) = $\frac{3}{2}$ - $\frac{1}{2}$n + $\frac{1}{2}$ = 2 - $\frac{1}{2}$ n
Indicated term $a_{30}$ = 2 - $\frac{1}{2}$ $\times$ 30 = 2 - 15 = -13
