Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.
To find $ a_{ 74 } $ we use formula
$$ \color{blue}{a_n = a_1 + (n-1)d}$$In this example we have $ a_1 = -3,~~ d = 5 ~~,~~ n = 74 $. After substituting these values into the formula, we obtain:
$$ \begin{aligned} a_n &= a_1 + d(n-1) \\[1 em] a_{ 74 } &= -3 + (74-1) \cdot 5 \\[1 em] a_{ 74 } &= -3 + 365 \\[1 em] a_{ 74 } &= 362 \end{aligned} $$The first few terms of this sequence are:
$$ -3, ~~~2, ~~~7, ~~~12, ~~~17 . . . $$