Respuesta :

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

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

How can the expression that represents the geometric series be found?

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

  • First term, a = 2

  • Common ratio, r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

Learn more about geometric series here:

https://brainly.com/question/2289626

#SPJ1