Common Difference in Sequences - SSAT Upper Level Quantitative (Math)
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Set R consists of multiples of 4. Which of the following sets are also included within set R?
Set R consists of multiples of 4. Which of the following sets are also included within set R?
The easiest way to solve this problem is to write out the first few numbers of the sets.
Set R (multiples of 4): 
Set W (multiples of 8): 
Set X (multiples of 2): 
Set Y (multiples of 6): 
Set Z (multiples of 1): 
Set Q (multiples of 7): 
Given that Set W is the only set in which the entire set of numbers is reflected in Set R, it is the correct answer.
The easiest way to solve this problem is to write out the first few numbers of the sets.
Set R (multiples of 4):
Set W (multiples of 8):
Set X (multiples of 2):
Set Y (multiples of 6):
Set Z (multiples of 1):
Set Q (multiples of 7):
Given that Set W is the only set in which the entire set of numbers is reflected in Set R, it is the correct answer.
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What number comes next in this sequence?
4 12 9 6 18 15 12 36 33 __
What number comes next in this sequence?
4 12 9 6 18 15 12 36 33 __
Determining sequences can take some trial and error, but generally aren't as intimidating as they may at first appear. For this sequence, you multiply the first term by 3, and then subtract 3 two times in a row. Then repeat. When you get to 33, you have only subtracted 3 once, so you have to do that one more time:
Determining sequences can take some trial and error, but generally aren't as intimidating as they may at first appear. For this sequence, you multiply the first term by 3, and then subtract 3 two times in a row. Then repeat. When you get to 33, you have only subtracted 3 once, so you have to do that one more time:
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What number comes next in the sequence?
_______
What number comes next in the sequence?
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with 
, we add 
to get 
, subtract 
to get 
, and then repeat.
When we get to 
for the second time in the sequence, we are adding 
to get 
. By the next step in the sequence, we will subtract 
to get the missing number 
.
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with
When we get to
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What is the next number in the sequence?
_______
What is the next number in the sequence?
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with 
, we add 
to get 
and then subtract 
to get 
.
By the time we get to 
, we have subtracted 
from 
to complete the cycle of common differences. We will therefore add 
to 
next, getting the missing number 
.
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with
By the time we get to
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What is the next number in the sequence?
_______
What is the next number in the sequence?
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting at the beginning, we multiply 
by 
to get 
and then divide by 
to get 
.
We multiply the second 
in the sequence by 
to get 
, so by the logic of the sequence we will be dividing by 
to get the missing number 
.
In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting at the beginning, we multiply
We multiply the second
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Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
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Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above
Find the common difference for the arithmetic sequence:
Find the common difference for the arithmetic sequence:
Subtract the first term from the second term to find the common difference.
Subtract the first term from the second term to find the common difference.
Compare your answer with the correct one above