All Precalculus Resources
Example Questions
Example Question #1 : Sigma Notation
Solve:
The summation starts at 2 and ends at 4. Write out the terms and solve.
The answer is:
Example Question #21 : Sequences And Series
Write the following series in sigma notation.
To write in sigma notation, let's make sure we have an alternating sign expression given by:
Now that we have the alternating sign, let's establish a function that increases by per term starting at . This is given by
Putting it all together,
Example Question #22 : Sequences And Series
Compute:
In order to solve this summation, substitute the bottom value of to the function, plus every integer until the iteration reaches to 5.
Example Question #11 : Sigma Notation
Evaluate:
To evaluate this, input the bottom integer into the expression . Repeat for every integer following the bottom integer until we reach to the top integer . Sum each iteration.
Add these terms for the summation.
Example Question #21 : Sequences And Series
What is the proper sigma sum notation of the summation of ?
Given that the first term of the sequence is , we know that the first term of the summation must be , and thus the lower bound of summation must be equal to There is only one option with this qualification, and so we have our answer.
Example Question #31 : Pre Calculus
Consider the sequence:
What is the fifteenth term in the sequence?
The sequence can be described by the equation , where is the term in the sequence.
For the 15th term, .
Example Question #1 : Terms In A Series
What is the sum of the first terms of an arithmetic series if the first term is , and the last term is ?
Write the formula to find the arithmetic sum of a series where is the number of terms, is the first term, and is the last term.
Substitute the given values and solve for the sum.
Example Question #3 : Terms In A Series
Given the terms of the sequence , what are the next two terms after ?
The next two terms are and . This is the Fibonacci sequence where you start off with the terms and , and the next term is the sum of two previous terms. So then
and so on.
Example Question #1 : Terms In A Series
What is the fifth term of the series
Let's try to see if this series is a geometric series.
We can divide adjacent terms to try and discover a multiplicative factor.
Doing this it seems the series proceeds with a common multiple of between each term.
Rewriting the series we get,
.
When
.
Example Question #22 : Sequences And Series
What is the 9th term of the series that begins 2, 4, 8, 16...
512
1024
256
488
144
512
In this geometric series, each number is created by multiplying the previous number by 2. You may also see that, because the first number is 2, it also becomes a list of powers of 2. The list is 2, 4, 8, 16, 32, 64, 128, 256, 512, where you can see that the 9th term is 512.