, , ,

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 gives the next term. In other words, .

Geometric Sequence:

This is the form of a geometric sequence.

Substitute in the values of and .

Remove parentheses.

This is the formula to find the sum of the first terms of the geometric sequence. To evaluate it, find the values of and .

Replace the variables with the known values to find .

Raise to the power of .

Subtract from .

Subtract from .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Convert the fraction to a decimal.

Find the Sum of the Series 3 , 12 , 48 , 192