, , ,

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 .

Apply the product rule to .

Apply the product rule to .

Combine and .

Combine and .

Substitute in the value of to find the th term.

Subtract from .

Raise to the power of .

Subtract from .

Raise to the power of .

Combine exponents.

Factor out negative.

Multiply by .

Multiply by .

Subtract from .

Raise to the power of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Find the 6th Term 4 , -3 , 9/4 , -27/16