# Calculus Examples

, ,

Step 1

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:

Step 2

This is the form of a geometric sequence.

Step 3

Substitute in the values of and .

Step 4

Apply the product rule to .

Step 5

Combine.

Step 6

Step 6.1

Multiply by .

Step 6.1.1

Raise to the power of .

Step 6.1.2

Use the power rule to combine exponents.

Step 6.2

Combine the opposite terms in .

Step 6.2.1

Subtract from .

Step 6.2.2

Add and .

Step 7

One to any power is one.

Step 8

Substitute in the value of to find the th term.

Step 9

Step 9.1

Subtract from .

Step 9.2

Raise to the power of .

Step 10

Multiply by .