Algebra II : Other Sequences and Series
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : Other Sequences And Series
Consider the following formula for a recursive sequence:
Which answer choice best represents this sequence?
2, 4, 16, 32, ...
2, 4, 6, 8, ...
2, 4, 8, 16, ....
2, 4, 16, 256, ...
2, 4, 16, 256, ...
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:
How many of the first twenty terms of the sequence are positive?
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:
Which of the following is the first positive term of the sequence?
The sequence has no positive terms.
Apply the rule to find the first few terms:
The first positive term of the sequence is 
Example Question #1 : Other Sequences And Series
Which of the following expressions describes the sequence below:
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.
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 #2 : Other Sequences And Series
What is the median of the following prices.
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 #1 : Other Sequences And Series
Complete the following sequences.
The sequence goes down by 2 so,
Therefore the next number in the sequence is 
Example Question #2 : Other Sequences And Series
Complete the following sequence
The sequence goes up by 5 so,
Therefore the next term in the sequence will be 
Example Question #3 : Other Sequences And Series
What is 
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 
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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