Find $ a_20 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.
To find $ a_{ 20 } $ we use formula
$$ \color{blue}{a_n = a_1 \cdot r^{n-1}}$$In this example we have $ a_1 = 2 ~~,~~ r = 3 ~~\text{and}~~ n = 20 $. After substituting these values to above formula, we obtain:
$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 20 } &= 2 \cdot 3^{ 20 - 1} \\ a_{ 20 } &= 2 \cdot 1162261467 \\ a_{ 20 } &= 2324522934 \end{aligned}$$The first few terms of this sequence are:
$$ 2, ~~~6, ~~~18, ~~~54 . . . $$