### All Precalculus Resources

## Example Questions

### Example Question #31 : Sequences And Series

What is the 10th term in the series:

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

**Possible Answers:**

37

23

41

45

31

**Correct answer:**

37

The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37

The correct answer, then, is 37.

### Example Question #1 : Partial Sums Of Series

For the sequence

Determine .

**Possible Answers:**

**Correct answer:**

is defined as the sum of the terms from to

Therefore, to get the solution we must add all the entries from from to as follows.

### Example Question #2 : Partial Sums Of Series

Simplify the sum.

**Possible Answers:**

**Correct answer:**

The answer is . Try this for :

This can be proven more generally using a proof technique called mathematical induction, which you will most likely not learn in high school.

### Example Question #3 : Partial Sums Of Series

In case you are not familiar with summation notation, note that:

Given the series above, what is the value of ?

**Possible Answers:**

**Correct answer:**

Since the upper bound of the iterator is and the initial value is , we need add one-half, the summand, six times.

This results in the following arithmetic.

### Example Question #1 : Partial Sums Of Series

In case you are not familiar with summation notation, note that:

What is the value of ?

**Possible Answers:**

**Correct answer:**

Because the iterator starts at , we first have a .

Now expanding the summation to show the step by step process involved in answering the question we get,

### Example Question #1 : Sums Of Infinite Series

Find the value for

**Possible Answers:**

**Correct answer:**

To best understand, let's write out the series. So

We can see this is an infinite geometric series with each successive term being multiplied by .

A definition you may wish to remember is

where stands for the common ratio between the numbers, which in this case is or . So we get

### Example Question #41 : Pre Calculus

Evaluate:

**Possible Answers:**

The series does not converge.

**Correct answer:**

This is a geometric series whose first term is and whose common ratio is . The sum of this series is:

### Example Question #2 : Sums Of Infinite Series

Evaluate:

**Possible Answers:**

The series does not converge.

**Correct answer:**

This is a geometric series whose first term is and whose common ratio is . The sum of this series is:

### Example Question #1 : Sums Of Infinite Series

What is the sum of the following infinite series?

**Possible Answers:**

diverges

**Correct answer:**

This series is not alternating - it is the mixture of two geometric series.

The first series has the positive terms.

The second series has the negative terms.

The sum of these values is 3.5.

### Example Question #3 : Sums Of Infinite Series

What is the sum of the alternating series below?

**Possible Answers:**

**Correct answer:**

The alternating series follows a geometric pattern.

We can evaluate the geometric series from the formula.