# Precalculus : Terms in a Series

## Example Questions

### Example Question #1 : Terms In A Series

Consider the sequence:

What is the fifteenth term in the sequence?

Explanation:

The sequence can be described by the equation , where is the term in the sequence.

For the 15th term, .

### Example Question #1 : Terms In A Series

What is the sum of the first  terms of an arithmetic series if the first term is , and the last term is ?

Explanation:

Write the formula to find the arithmetic sum of a series where  is the number of terms,  is the first term, and  is the last term.

Substitute the given values and solve for the sum.

### Example Question #1 : Terms In A Series

Given the terms of the sequence , what are the next two terms after ?

Explanation:

The next two terms are  and . This is the Fibonacci sequence where you start off with the terms  and , and the next term is the sum of two previous terms. So then

and so on.

### Example Question #3 : Terms In A Series

What is the fifth term of the series

Explanation:

Let's try to see if this series is a geometric series.

We can divide adjacent terms to try and discover a multiplicative factor.

Doing this it seems the series proceeds with a common multiple of  between each term.

Rewriting the series we get,

.

When

.

### Example Question #1 : Terms In A Series

What is the 9th term of the series that begins 2, 4, 8, 16...

256

512

488

144

1024

512

Explanation:

In this geometric series, each number is created by multiplying the previous number by 2.  You may also see that, because the first number is 2, it also becomes a list of powers of 2.  The list is 2, 4, 8, 16, 32, 64, 128, 256, 512, where you can see that the 9th term is 512.

### Example Question #2 : Terms In A Series

What is the 10th term in the series:

1, 5, 9, 13, 17....

31

37

45

23

41