Algebra II : Other Sequences and Series

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Other Sequences And Series

Consider the following formula for a recursive sequence:

Which answer choice best represents this sequence?

Possible Answers:

2, 4, 16, 256, ...

2, 4, 16, 32, ...

2, 4, 6, 8, ...

2, 4, 8, 16, ....

Correct answer:

2, 4, 16, 256, ...

Explanation:

A recursive formula creates a sequence where each term is defined by the term(s) that precede it. In other words, in order to know term 12, you have to know term 11, etc.

The problem already tells us that the first term is 2. Let's find the second term.

We continue to find the rest of the terms in this way.

Example Question #2 : Other Sequences And Series

A sequence is defined recursively as follows:

 for 

How many of the first twenty terms of the sequence are positive?

Possible Answers:

Correct answer:

Explanation:

Apply the rule to find the first few terms:

After the sixth term, it is apparent that this cycle will repeat itself, so the first twenty terms of the sequence will be, in order:

Seven of these first twenty terms are positive.

Example Question #3 : Other Sequences And Series

A sequence is defined recursively as follows:

 for 

Which of the following is the first positive term of the sequence?

Possible Answers:

The sequence has no positive terms.

Correct answer:

Explanation:

Apply the rule to find the first few terms:

The first positive term of the sequence is .

 

Example Question #4 : Other Sequences And Series

Which of the following expressions describes the sequence below:

Possible Answers:

Correct answer:

Explanation:

In order to determine which expression describes the sequence in the problem, we must determine the relationship each entry has with its position in the sequence. For example, for n=1, we must determine which expression involving n will yield a result of 3, for n=2, we must determine which expression will yield a result of 8, and so on, ensuring that the expression holds true for every n value in the sequence. If we check each of our answers, we can see that only the following expression will give the correct result for each increasing value of n:

If we continue, we can see that we will obtain the sequence 3,8,15,24,35,48,63,..., so this expression is the correct representation of the sequence given in the problem.

Example Question #3 : Other Sequences And Series

What is the mean of the following quiz scores.

Possible Answers:

Correct answer:

Explanation:

To find the mean of a set of numbers we first must add all the numbers together.

Using the formula for mean we get,

 

Therefore we get,

Example Question #6 : Other Sequences And Series

What is the median of the following prices.

 

Possible Answers:

Correct answer:

Explanation:

The median of a set of numbers is the middle value of the set.

To find the middle value of this particular data set put the prices in order of lowest to highest

Since we have an even number of entries we will need to find the mean of the two middle numbers and this will become our median.

Example Question #7 : Other Sequences And Series

Complete the following sequences.

Possible Answers:

Correct answer:

Explanation:

The sequence goes down by 2 so,

 .

Therefore the next number in the sequence is .

Example Question #8 : Other Sequences And Series

Complete the following sequence

Possible Answers:

Correct answer:

Explanation:

The sequence goes up by 5 so,

 

Therefore the next term in the sequence will be .

Example Question #9 : Other Sequences And Series

What is percent of ?

Possible Answers:

Correct answer:

Explanation:

To find the value related to the specific percentage we need to set up a proportion and solve for x.

From here we cross multiply and divide to find the value of x.

Example Question #10 : Other Sequences And Series

What is percent of ?

Possible Answers:

Correct answer:

Explanation:

To find the value for a specific percentage of a number we first need to convert the percentage into a decimal.

From here we multiply the decimal with the number we are given in the question.

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