Sequences and Series - SSAT Upper Level Quantitative
Card 0 of 252
Which of the following can be the sum of four consecutive positive integers?
Which of the following can be the sum of four consecutive positive integers?
Let 
, 
, 
, and 
be the four consecutive integers. Then their sum would be
In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.
Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.
Let
In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.
Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.
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Three consecutive integers have sum 
. What is their product?
Three consecutive integers have sum
Let the middle integer of the three be 
. The three integers are therefore
, and they can be found using the equation
This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.
Let the middle integer of the three be
This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.
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Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?
Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?
Let the middle integer of the three be 
. The three integers are therefore
, and they can be found using the equation
The three integers are 177, 179, and 181, and the product of the least and greatest is
Let the middle integer of the three be
The three integers are 177, 179, and 181, and the product of the least and greatest is
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Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?
Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?
Let the middle integer of the three be 
. The three integers are therefore
, and they can be found using the equation
The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is
Let the middle integer of the three be
The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is
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Four consecutive integers have sum 3,350. What is the product of the middle two?
Four consecutive integers have sum 3,350. What is the product of the middle two?
Call the least of the four integers 
. The four integers are therefore
,
and they can be found using the equation
The integers are 836, 837, 838, 839.
To get the correct response, multiply:
Call the least of the four integers
and they can be found using the equation
The integers are 836, 837, 838, 839.
To get the correct response, multiply:
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Three consecutive integers have a sum of 
. What is their product?
Three consecutive integers have a sum of
Let the middle integer of the three be 
. The three integers are therefore
, and they can be found using the equation
The integers are therefore 103, 104, 105. The correct response is their product, which is
Let the middle integer of the three be
The integers are therefore 103, 104, 105. The correct response is their product, which is
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What is the value of 
is this sequence?
What is the value of
This is a geometric sequence since the pattern of the sequence is through multiplication.
You have to multiple each value by 
to get the next one.
The value before 
is 
so 
.
This is a geometric sequence since the pattern of the sequence is through multiplication.
You have to multiple each value by
The value before
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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.
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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.
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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.
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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