Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
Given the the sequence below, what is the 11th term of the sequence?
1, 5, 9, 13, . . .
45
49
53
41
37
41
The 11th term means there are 10 gaps in between the first term and the 11th term. Each gap has a difference of +4, so the 11th term would be given by 10 * 4 + 1 = 41.
The first term is 1.
Each term after increases by +4.
The nth term will be equal to 1 + (n – 1)(4).
The 11th term will be 1 + (11 – 1)(4)
1 + (10)(4) = 1 + (40) = 41
Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence
The second term of an arithmetic sequence is 
The common difference between the terms is half that between the second and fourth terms - that is:
Subtract this common difference from the second term to get the first:
Example Question #12 : How To Find The Nth Term Of An Arithmetic Sequence
An arithmetic sequence is given by the formula 
You can either calculate the vaules of 
Example Question #81 : Mathematical Relationships And Basic Graphs
Consider the following arithmetic sequence:
What is the 
A simple way to find the 
Here, 
Example Question #11 : Counting / Sets
Which number is needed to complete the following sequence:
1,5,_,13,17
This is a sequence that features every other positive, odd integers. The missing number in this case is 9.
Example Question #81 : Mathematical Relationships And Basic Graphs
Find the next term in the following arithmetic series:
Find the next term in the following arithmetic series:
To find the next term in an arithmetic series, we need to find the common difference. To do so, find the difference between any two consecutive terms in the sequence:
Our common difference is 7. Now we need to add that to the last term to get what we want
So our next term is 32
Example Question #81 : Mathematical Relationships And Basic Graphs
What is the common difference of the following arithmetic series?
What is the common difference of the following arithmetic series?
To find the common difference, we need to find the difference between any two consecutive terms.
Try with the first two:
To be sure, try it with the 2nd and 3rd
We keep getting the same thing, -8. It must be negative, because our sequence is decreasing. Therefore, we have our answer: -8
Example Question #21 : Arithmetic Series
What is the 16th term in the sequence that starts with 7, 4, 1, ...?
The sequence is decreasing by 3 each term. To get from the first term to the 16th term, you must subtract 3 fifteen times:
Example Question #84 : Mathematical Relationships And Basic Graphs
Solve the series:
Write the n-th term formula.
The 
The 
Solve for 
Divide by two on both sides.
The formula for n-terms in a arithmetic sequence is:
Substitute the known terms.
The answer is:
Example Question #82 : Summations And Sequences
Determine the sum of:
Write the formula for the sum of an arithmetic series.
To determine the value of 
Divide by five on both sides.
Substitute all the terms into the sum formula.
The answer is:
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