# High School Math : Using Sigma Notation

## Example Questions

### Example Question #1 : Using Sigma Notation

Determine the summation notation for the following series:

Explanation:

The series is a geometric series. The summation notation of a geometric series is

,

where  is the number of terms in the series,  is the first term of the series, and  is the common ratio between terms.

In this series,  is  is , and  is . Therefore, the summation notation of this geometric series is:

This simplifies to:

### Example Question #5 : Sequences And Series

Determine the summation notation for the following series:

Explanation:

The series is a geometric series. The summation notation of a geometric series is

,

where  is the number of terms in the series,  is the first term of the series, and  is the common ratio between terms.

In this series,  is  is , and  is . Therefore, the summation notation of this geometric series is:

This simplifies to:

### Example Question #6 : Sequences And Series

Indicate the sum of the following series:

Explanation:

The formula for the sum of an arithmetic series is

,

where  is the first value in the series,  is the number of terms in the series, and  is the difference between sequential terms in the series.

In this problem we have:

Plugging in our values, we get:

### Example Question #2 : Sequences And Series

Indicate the sum of the following series:

Explanation:

The formula for the sum of an arithmetic series is

,

where  is the first value in the series,  is the number of terms in the series, and  is the difference between sequential terms in the series.

Here we have:

Plugging in our values, we get:

### Example Question #8 : Sequences And Series

Indicate the sum of the following series:

Explanation:

The formula for the sum of a geometric series is

,

where  is the first term in the series,  is the rate of change between sequential terms, and  is the number of terms in the series

For this problem, these values are:

Plugging in our values, we get:

### Example Question #11 : Sequences And Series

Indicate the sum of the following series.