How to find the next term in an arithmetic sequence - SAT Math
Card 0 of 11
A sequence of numbers is as follows:
What is the sum of the first seven numbers in the sequence?
A sequence of numbers is as follows:
What is the sum of the first seven numbers in the sequence?
The pattern of the sequence is (x+1) * 2.
We have the first 5 terms, so we need terms 6 and 7:
(78+1) * 2 = 158
(158+1) * 2 = 318
3 + 8 + 18 +38 + 78 + 158 + 318 = 621
The pattern of the sequence is (x+1) * 2.
We have the first 5 terms, so we need terms 6 and 7:
(78+1) * 2 = 158
(158+1) * 2 = 318
3 + 8 + 18 +38 + 78 + 158 + 318 = 621
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What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?
What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?
The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.
The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.
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Each term in the sequence is one less than twice the previous term.
So, 
Each term in the sequence is one less than twice the previous term.
So,
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Find the next term of the following sequence:
Find the next term of the following sequence:
The sequence provided is arithmetic. An arithmetic sequence has a common difference between each consecutive term. In this case, the difference is 
; therefore, the next term is 
.
You can also use a formula to find the next term of an arithmetic sequence:
where 
the current term and 
the common difference.
The sequence provided is arithmetic. An arithmetic sequence has a common difference between each consecutive term. In this case, the difference is
You can also use a formula to find the next term of an arithmetic sequence:
where
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Solve each problem and decide which is the best of the choices given.
Find the sixth term in the following arithmetic sequence.
Solve each problem and decide which is the best of the choices given.
Find the sixth term in the following arithmetic sequence.
First find the common difference of the sequence,
Thus there is a common difference of
between each term,
so follow that pattern for another 
terms, and the result is 
.
First find the common difference of the sequence,
Thus there is a common difference of
so follow that pattern for another
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Find the missing number in the sequence:
Find the missing number in the sequence:
The pattern of this sequence is 
where 
represents the position of the number in the sequence.
for the first number in the sequence.
for the second number.
For the fourth term, 
. Therefore, 
.
The pattern of this sequence is
For the fourth term,
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Complete the sequence:
Complete the sequence:
The pattern of this sequence is 
where 
represents the place of each number in the order of the sequence.
Here are our givens:
, our first term.
, our second term.
, our third term.
This means that our fourth term will be:
.
The pattern of this sequence is
Here are our givens:
This means that our fourth term will be:
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An arithmetic sequence begins as follows:
Express the next term of the sequence in simplest radical form.
An arithmetic sequence begins as follows:
Express the next term of the sequence in simplest radical form.
Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:
The common difference 
of an arithmetic sequence can be found by subtracting the first term from the second:
Add this to the second term to obtain the desired third term:
.
Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:
The common difference
Add this to the second term to obtain the desired third term:
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An arithmetic sequence begins as follows:
Give the sixth term of the sequence.
An arithmetic sequence begins as follows:
Give the sixth term of the sequence.
The common difference 
of an arithmetic sequence can be found by subtracting the first term from the second:
Setting 
:
The 
th term 
of an arithmetic sequence can be derived using the formula
Setting 
The common difference
Setting
The
Setting
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An arithmetic sequence begins as follows:
Give the next term of the sequence in simplest radical form.
An arithmetic sequence begins as follows:
Give the next term of the sequence in simplest radical form.
Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.
The common difference 
of an arithmetic sequence can be found by subtracting the first term from the second:
Setting 
:
Add this to the second term to obtain the desired third term:
This is not among the given choices.
Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.
The common difference
Setting
Add this to the second term to obtain the desired third term:
This is not among the given choices.
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An arithmetic sequence begins as follows:
Give the sixth term of the sequence in decimal form.
An arithmetic sequence begins as follows:
Give the sixth term of the sequence in decimal form.
The common difference of an arithmetic sequence can be found by subtracting the first term from the second:
Setting 
:
The th term of an arithmetic sequence can be derived using the formula
Setting 
:
The decimal equivalent of this can be found by dividing 13 by 15 as follows:
The correct choice is 
.
The common difference
Setting
The
Setting
The decimal equivalent of this can be found by dividing 13 by 15 as follows:
The correct choice is
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