Algebra II : Arithmetic Series
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Example Questions
Example Question #31 : Arithmetic Series
For the sequence of numbers 
a) An explicit formula for the nth term
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a) The general formula for an arithmetic sequence of terms 
For the sequence to be a true arithmetic sequence, the common difference must be the same for any two adjacent terms in the sequence.
For our sequence:
and so on...
An explicit formula can now be written,
We can now test this formula for the first few terms (columns 1-3 in the table below).
b) In the table below, columns 4-5 show the calculations for the 
Example Question #32 : Arithmetic Series
An arithmetic sequence begins as follows:
Which of the following gives the definition of its 
The 
where 
and
Substituting, the expression becomes
Simplify this:
Example Question #33 : Arithmetic Series
List the first five terms 
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a) First we will start with creating the list of consecutive odd integers with the required relationships satisfied.
Start by calling the first of these five integers 
Now we need to translate the conditions given in the text of the problem into a mathematical expression. Write it out piece-by-piece. First let's right out these two statements separately,
...the sum of the 2nd plus 3-times the first...
...the sum of the 3rd integer plus 2-times the 5th integer...
In the text of the problem the first quantity "is one less than" the other quantity. In other words, the quantity 
Now solve for 
Now we can use this solution to find the other four integers:
b) Now that we have the first 5 terms, 
Where 
Example Question #34 : Arithmetic Series
A sequence begins as follows:
Which statement is true?
The sequence may be arithmetic and geometric.
The sequence may be geometric.
The sequence cannot be arithmetic or geometric.
None of these
The sequence may be arithmetic.
The sequence may be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one is not constant:
These ratios can be immediately seen to be unequal as they are of different sign.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the difference between each term and the previous term is the same:
The sequence could be arithmetic.
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