The function that gives the value of <em>tn</em> for the geometric series is presented as follows;

<h3>How can the expression that represents the geometric series be found?</h3>
The given geometric series is presented as follows;
2 + 6 + 18 + 54 +...
From the above series, we have;
- First term, <em>a</em> = 2
- Common ratio, <em>r </em>= 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3
The nth term of the geometric series is therefore;

Which gives;

Where, tn is the nth term
Learn more about geometric series here:
brainly.com/question/2289626
#SPJ1