Algebra II : Summations and Sequences
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #31 : Mathematical Relationships And Basic Graphs
The Fibonacci sequence is given as
.
.
.
Find
In other words,
As such, the asnwer is 
Example Question #32 : Mathematical Relationships And Basic Graphs
Calculate:
The sigma notation indicates summation starting from 1 and ends at 4.
Substitute in order of the iteration.
The correct answer is 
Example Question #33 : Mathematical Relationships And Basic Graphs
Summation (Sigma) Notation
Rewrite the below series in summation or sigma notation:
First we must write an equation for the pattern in the series. We can see that this is an arithmetic pattern because the same number (4) is being added each time.
The formula to write the rule or equation for an arithmetic pattern is:
Where a1 is the first value in the sequence and d is the common difference, n is left as a variable.
When we plug in the values we are given we get:
Which simplifies to become:
Which further simplifies to become:
Now we must put this in the sigma or summation notation.
We know that summation notation always involves the greek letter sigma
The number on the bottom is the first number that is plugged in, first input or first domain number - in this case it is 1.
The number on top is the last number that is plugged in, the last input or the number of numbers in the series - there are five numbers in this series, so it ends with 5.
So the final summation will look like this:
Example Question #34 : Mathematical Relationships And Basic Graphs
Solve:
Evaluate each summation term first.
The bottom number is the first term of the summation. Plug the number into the expression. Repeat the summation for every whole number until the summation reaches the top number.
Evaluate the next summation.
Subtract this value from the value of the first summation.
The answer is:
Example Question #35 : Mathematical Relationships And Basic Graphs
Solve:
To evaluate this summation, first ignore the outside negative sign and substitute the bottom value into the quantity inside the summation. Reiterate for every integer after zero until we reach the top integer.
Simplify.
Therefore:
The answer is 
Example Question #36 : Mathematical Relationships And Basic Graphs
Evaluate:
The summation will loop from 
Rewrite the summation.
The answer is:
Example Question #37 : Mathematical Relationships And Basic Graphs
Evaluate:
In order to evaluate this summation, expand the terms. Start by plugging in zero into 
Simplify the terms by order of operations.
Evaluate the terms inside the parentheses first.
The answer is:
Example Question #38 : Mathematical Relationships And Basic Graphs
Evaluate:
In order to solve the summation, expand the terms of the binomial. Substitute two first, and add the quantities of each term for each integer repeating until the top integer is reached.
The answer is:
Example Question #11 : Sigma Notation
Evaluate:
Write out the terms of the sigma notation. This will repeat for the second to the fifth term. There is no variable to substitute, which means that after every iteration, the value that is summed is two.
The answer is:
Example Question #40 : Mathematical Relationships And Basic Graphs
Evaluate:
In order to evaluate the summation, substitute the bottom number into the quantity, and repeat for every integer after the eight and up to the top number, ten.
Evaluate each term and simplify.
The answer is:
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