A geometric sequence is given the by equation $\displaystyle {L}{\left({n}\right)}={200}\cdot{1.12}^{{n}}$ Find the sum of the first 38 terms of this sequence.

What is the common ratio for this sequence?
$\displaystyle {r}$ =

What is the index of the final term of this sum?
last index =

What is the sum?
Sum =