, , , ,

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 .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Combine the opposite terms in .

Subtract from .

Add and .

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 .

Divide by .

Multiply by .

Convert the fraction to a decimal.

Find the Sum of the Series 4 , 16 , 64 , 256 , 1024