Find the Sum of the Series 4 , 12 , 36 , 108

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by ${\displaystyle 3}$ gives the next term. In other words, ${\displaystyle a_n=a_1\cdot r^{n-1}}$.

Geometric Sequence: ${\displaystyle r=3}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=4}$ and ${\displaystyle r=3}$.

Remove parentheses.

This is the formula to find the sum of the first ${\displaystyle n}$ terms of the geometric sequence. To evaluate it, find the values of ${\displaystyle r}$ and ${\displaystyle a_1}$.

Replace the variables with the known values to find ${\displaystyle S_4}$.