Finding Terms in a Series - High School Math
Card 0 of 8
Consider the sequence: 
What is the fifteenth term in the sequence?
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, 
.
The sequence can be described by the equation
For the 15th term,
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What is the sixth term when 
is expanded?
What is the sixth term when
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:
,
where 
is 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 let 
and 
. 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 
.
We will need to use the Binomial Theorem in order to solve this problem. Consider the expansion of
where
We are asked to find the sixth term of
Next, let's find the value of
Remember that, if n is a positive integer, then
Let's go back to simplifying
The answer is
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What are the first three terms in the series?
What are the first three terms in the series?
To find the first three terms, replace 
with 
, 
, and 
.
The first three terms are 
, 
, and 
.
To find the first three terms, replace
The first three terms are
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Find the first three terms in the series.
Find the first three terms in the series.
To find the first three terms, replace with 
, 
, and 
.
The first three terms are 
, 
, and 
.
To find the first three terms, replace
The first three terms are
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Indicate the first three terms of the following series:
Indicate the first three terms of the following series:
In the arithmetic series, the first terms can be found by plugging 
, 
, and 
into the equation.
In the arithmetic series, the first terms can be found by plugging
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Indicate the first three terms of the following series:
Indicate the first three terms of the following series:
In the arithmetic series, the first terms can be found by plugging in 
, 
, and 
for 
.
In the arithmetic series, the first terms can be found by plugging in
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Indicate the first three terms of the following series:
Indicate the first three terms of the following series:
The first terms can be found by substituting 
, 
, and 
for 
into the sum formula.
The first terms can be found by substituting
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Indicate the first three terms of the following series.
Indicate the first three terms of the following series.
The first terms can be found by substituting 
, 
, and 
in for 
.
The first terms can be found by substituting
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