# Calculus 2 : Arithmetic and Geometric Series

## Example Questions

### Example Question #11 : Arithmetic And Geometric Series

Calculate the sum of the following series:

Explanation:

This is an arithmetic series.

Its general form is

To calculate the sum of very large series such as these, use the formula

This works because you are taking the average of the largest and smallest terms, and then multiplying them by n, which is the same as calculating the sum total.

When k is not equal to 1, split the sums up into 2 piece and take the difference.

Find

Solution:

### Example Question #12 : Arithmetic And Geometric Series

Calculate the sum of the following series:

Explanation:

This is an arithmetic series.

Its general form is

To calculate the sum of very large series such as these, use the formula

This works because you are taking the average of the largest and smallest terms, and then multiplying them by n, which is the same as calculating the sum total.

When k is not equal to 1, split the sums up into 2 piece and take the difference.

Find

Solution:

### Example Question #13 : Arithmetic And Geometric Series

Calculate the sum of the following series:

Explanation:

This is an arithmetic series.

Its general form is

To calculate the sum of very large series such as these, use the formula

This works because you are taking the average of the largest and smallest terms, and then multiplying them by n, which is the same as calculating the sum total.

When k is not equal to 1, split the sums up into 2 piece and take the difference.

Find

Solution:

### Example Question #14 : Arithmetic And Geometric Series

Find the value of the 700th term, or , in the following arithmetic series:

Explanation:

3 pieces of information are needed to find the value of a specific term

First, find the first value, .

Second, the value of n, or the total number of terms in the series.

Finally, d, or the common difference, which can be found by calculating .

With these pieces of information, find the value of the last with the following formula:

Solution:

### Example Question #15 : Arithmetic And Geometric Series

Find the value of the 400th term, or , in the following arithmetic series:

Explanation:

3 pieces of information are needed to find the value of a specific term.

First, find the first value, .

Second, the value of n, or the total number of terms in the series.

Finally, d, or the common difference, which can be found by calculating .

With these pieces of information, find the value of the last with the following formula:

Solution:

### Example Question #11 : Types Of Series

Find the value of the 1200th term, or , in the following arithmetic series:

Explanation:

3 pieces of information are needed to find the value of a specific term.

First, find the first value, .

Second, the value of n, or the total number of terms in the series.

Finally, d, or the common difference, which can be found by calculating .

With these pieces of information, find the value of the last with the following formula:

Solution:

### Example Question #17 : Arithmetic And Geometric Series

Find the value of the 300th term, or , in the following arithmetic series:

Explanation:

3 pieces of information are needed to find the value of a specific term.

First, find the first value, .

Second, the value of n, or the total number of terms in the series.

Finally, d, or the common difference, which can be found by calculating .

With these pieces of information, find the value of the last with the following formula:

Solution:

### Example Question #18 : Arithmetic And Geometric Series

Calculate the sum of a geometric series with the following values:,,. Round the answer to the nearest integer.

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

For this question, we are given all of the information we need.

Solution:

Rounding,

### Example Question #19 : Arithmetic And Geometric Series

Calculate the sum, rounded to the nearest integer, of the first 20 terms of the following geometric series:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

We have  and n and we just need to find r before calculating the sum.

Solution:

### Example Question #20 : Arithmetic And Geometric Series

Calculate the sum, rounded to the nearest integer, of the first 16 terms of the following geometric series:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

We have  and n and we just need to find r before calculating the sum.

Solution: