Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.
To find $ a_{ 0 } $ we use formula
$$ \color{blue}{a_n = a_1 + (n-1)d}$$In this example we have $ a_1 = 3,~~ d = 0 ~~,~~ n = 0 $. After substituting these values into the formula, we obtain:
$$ \begin{aligned} a_n &= a_1 + d(n-1) \\[1 em] a_{ 0 } &= 3 + (0-1) \cdot 0 \\[1 em] a_{ 0 } &= 3 + 0 \\[1 em] a_{ 0 } &= 3 \end{aligned} $$The first few terms of this sequence are:
$$ 3, ~~~3, ~~~3, ~~~3, ~~~3 . . . $$