To find $ a_{ 0 } $ we use formula

$$ \color{blue}{a_n = a_1 + (n-1)d}$$

In this example we have $ a_1 = 0,~~ d = \frac{ 1 }{ 2 } ~~,~~ n = 0 $. After substituting these values into the formula, we obtain:

$$ \begin{aligned} a_n &= a_1 + d(n-1) \\[1 em] a_{ 0 } &= 0 + (0-1) \cdot \frac{ 1 }{ 2 } \\[1 em] a_{ 0 } &= 0 + \left( -\frac{ 1 }{ 2 } \right) \\[1 em] a_{ 0 } &= -\frac{ 1 }{ 2 } \end{aligned} $$

The first few terms of this sequence are:

$$ 0, ~~~\frac{ 1 }{ 2 }, ~~~1, ~~~\frac{ 3 }{ 2 }, ~~~2 . . . $$

Arithmetic sequences