All High School Math Resources
Example Questions
Example Question #26 :Sequences And Series
Consider the sequence:
What is the fifteenth term in the sequence?
The sequence can be described by the equation, whereis the term in the sequence.
For the 15th term,.
Example Question #1 :Finding Terms In A Series
What are the first three terms in the series?
To find the first three terms, replacewith,, and.
The first three terms are,, and.
Example Question #1 :Finding Terms In A Series
Find the first three terms in the series.
To find the first three terms, replacewith,, and.
The first three terms are,, and.
Example Question #3 :Finding Terms In A Series
Indicate the first three terms of the following series:
In the arithmetic series, the first terms can be found by plugging,, andinto the equation.
Example Question #1 :Finding Terms In A Series
Indicate the first three terms of the following series:
In the arithmetic series, the first terms can be found by plugging in,, andfor.
Example Question #11 :Sequences And Series
Indicate the first three terms of the following series:
The first terms can be found by substituting,, andforinto the sum formula.
Example Question #6 :Finding Terms In A Series
Indicate the first three terms of the following series.
Not enough information
The first terms can be found by substituting,, andin for.
Example Question #11 :Sequences And Series
What is the sixth term whenis expanded?
We will need to use the Binomial Theorem in order to solve this problem. Consider the expansion of, where n is an integer. The rth term of this expansion is given by the following formula:
,
whereis a combination. In general, if x and y are nonnegative integers such that x > y, then the combination of x and y is defined as follows:.
We are asked to find the sixth term of, which means that in this case r = 6 and n = 10. Also, we will letand. We can now apply the Binomial Theorem to determine the sixth term, which is as follows:
Next, let's find the value of. According to the definition of a combination,
.
Remember that, if n is a positive integer, then. This is called a factorial.
Let's go back to simplifying.
The answer is.