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

, , ,
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 .
Simplify the numerator.
Raise to the power of .
Subtract from .
Reduce the expression by cancelling the common factors.
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