Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = 7 $.
To find $ a_{ 70 } $ we use formula
$$ \color{blue}{a_n = a_1 + (n-1)d}$$In this example we have $ a_1 = -26,~~ d = 7 ~~,~~ n = 70 $. After substituting these values into the formula, we obtain:
$$ \begin{aligned} a_n &= a_1 + d(n-1) \\[1 em] a_{ 70 } &= -26 + (70-1) \cdot 7 \\[1 em] a_{ 70 } &= -26 + 483 \\[1 em] a_{ 70 } &= 457 \end{aligned} $$The first few terms of this sequence are:
$$ -26, ~~~-19, ~~~-12, ~~~-5, ~~~2 . . . $$