Algebra II : Summations and Sequences
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #11 : Arithmetic Series
An arithmetic sequence is given by the formula 
You can either calculate the vaules of 
Example Question #13 : How To Find The Nth Term Of An Arithmetic Sequence
Consider the following arithmetic sequence:
What is the 
A simple way to find the 
Here, 
Example Question #5 : How To Find The Missing Number In A Set
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 #21 : Arithmetic Series
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 #22 : Arithmetic Series
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 #24 : Arithmetic Series
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 #25 : Arithmetic Series
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:
Example Question #26 : Arithmetic Series
Determine the sum of:
Write the formula to determine the sum of an arithmetic series.
where 
Use the following formula to determine how many terms are in this series.
The term 
Substitute the known values and solve for n.
Subtract two from both sides, and distribute the five through the binomial.
Add five on both sides.
Divide by five.
Plug this value and the other givens to the sum formula to determine the sum.
The answer is:
Example Question #27 : Arithmetic Series
If the first term is 4, and the common difference is 3, what is the formula for the sequence?
This represents an arithmetic sequence. Write the formula.
Substitute the first term and the common difference in the formula.
Simplify the terms.
The answer is:
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