Terms in a Series - Pre-Calculus
Card 0 of 6
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 sum of the first 
terms of an arithmetic series if the first term is 
, and the last term is 
?
What is the sum of the first
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.
Write the formula to find the arithmetic sum of a series where
Substitute the given values and solve for the sum.
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What is the fifth term of the 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
.
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
Rewriting the series we get,
When
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Given the terms of the sequence 
, what are the next two terms after 
?
Given the terms of the sequence
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.
The next two terms are
and so on.
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What is the 9th term of the series that begins 2, 4, 8, 16...
What is the 9th term of the series that begins 2, 4, 8, 16...
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.
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.
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What is the 10th term in the series:
1, 5, 9, 13, 17....
What is the 10th term in the series:
1, 5, 9, 13, 17....
The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37
The correct answer, then, is 37.
The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37
The correct answer, then, is 37.
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