### All High School Math Resources

## Example Questions

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

Consider the sequence:

What is the fifteenth term in the sequence?

**Possible Answers:**

**Correct answer:**

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

For the 15th term, .

### Example Question #11 : Sequences And Series

What are the first three terms in the series?

**Possible Answers:**

**Correct answer:**

To find the first three terms, replace with , , and .

The first three terms are , , and .

### Example Question #12 : Sequences And Series

Find the first three terms in the series.

**Possible Answers:**

**Correct answer:**

To find the first three terms, replace with , , and .

The first three terms are , , and .

### Example Question #13 : Sequences And Series

Indicate the first three terms of the following series:

**Possible Answers:**

**Correct answer:**

In the arithmetic series, the first terms can be found by plugging , , and into the equation.

### Example Question #14 : Sequences And Series

Indicate the first three terms of the following series:

**Possible Answers:**

**Correct answer:**

In the arithmetic series, the first terms can be found by plugging in , , and for .

### Example Question #15 : Sequences And Series

Indicate the first three terms of the following series:

**Possible Answers:**

**Correct answer:**

The first terms can be found by substituting , , and for into the sum formula.

### Example Question #16 : Sequences And Series

Indicate the first three terms of the following series.

**Possible Answers:**

Not enough information

**Correct answer:**

The first terms can be found by substituting , , and in for .

### Example Question #17 : Sequences And Series

What is the sixth term when is expanded?

**Possible Answers:**

**Correct answer:**

We will need to use the Binomial Theorem in order to solve this problem. Consider the expansion of , where n is an integer. The rth term of this expansion is given by the following formula:

,

where is a combination. In general, if x and y are nonnegative integers such that x > y, then the combination of x and y is defined as follows: .

We are asked to find the sixth term of , which means that in this case r = 6 and n = 10. Also, we will let and . We can now apply the Binomial Theorem to determine the sixth term, which is as follows:

Next, let's find the value of . According to the definition of a combination,

.

Remember that, if n is a positive integer, then . This is called a factorial.

Let's go back to simplifying .

The answer is .