High School Math : Finding Terms in a Series

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #184 : Pre Calculus

Consider the sequence:

What is the fifteenth term in the sequence?

Possible Answers:

Correct answer:

Explanation:

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

For the 15th term, .

Example Question #1 : Finding Terms In A Series

What are the first three terms in the series?

Possible Answers:

Correct answer:

Explanation:

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

The first three terms are , and .

Example Question #2 : Finding Terms In A Series

Find the first three terms in the series.

Possible Answers:

Correct answer:

Explanation:

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

The first three terms are , and .

Example Question #3 : Finding Terms In A Series

Indicate the first three terms of the following series:

Possible Answers:

Correct answer:

Explanation:

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

 

 

 

Example Question #4 : Finding Terms In A Series

Indicate the first three terms of the following series:

Possible Answers:

Correct answer:

Explanation:

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

 

 

 

Example Question #5 : Finding Terms In A Series

Indicate the first three terms of the following series:

Possible Answers:

Correct answer:

Explanation:

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

 

 

 

Example Question #2061 : High School Math

Indicate the first three terms of the following series.

Possible Answers:

Not enough information

Correct answer:

Explanation:

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

 

 

 

Example Question #2062 : High School Math

What is the sixth term when  is expanded?

Possible Answers:

Correct answer:

Explanation:

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 .

 

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