Which of the following cannot be three consecutive terms of an arithmetic sequence?
Possible Answers:
23,45,69
23,44,65
33,55,77
54,32,10
18,30,42
Correct answer:
23,45,69
Explanation:
In each group of numbers, compare the difference of the second and first terms to that of the third and second terms. The group in which they are unequal is the correct choice.
54,32,10:32−54=−22=10−32
23,44,65:44−23=21=65−44
33,55,77:55−33=22=77−55
18,30,42:30−18=12=42−30
23,45,69:45−23=22≠24=69−45
The last group of numbers is the correct choice.
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Find The Common Difference In Sequences : Example Question #2
Consider the arithmetic sequence
{2n+4,n2−3,6n,9n−7,9n+1}.
If n=5, find the common difference between consecutive terms.
Possible Answers:
−7
1
12
4
8
Correct answer:
8
Explanation:
In arithmetic sequences, the common difference is simply the value that is added to each term to produce the next term of the sequence. When solving this equation, one approach involves substituting 5 for n to find the numbers that make up this sequence. For example,
2(5)+4=14
so 14 is the first term of the sequence. However, a much easier approach involves only the last two terms, 9n−7 and 9n+1.
The difference between these expressions is 8, so this must be the common difference between consecutive terms in the sequence.
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Find The Common Difference In Sequences : Example Question #3
Find the common difference in the following arithmetic sequence.
{16,32,48,64...}
Possible Answers:
32
0
16
2
4
Correct answer:
16
Explanation:
An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.
32−16=16
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Find The Common Difference In Sequences : Example Question #4
Find the common difference in the following arithmetic sequence.
{54,27,0,−27...}
Possible Answers:
−1
0
−27
−54
27
Correct answer:
−27
Explanation:
An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.
27−54=−27
(i.e. the sequence advances by subtracting 27)
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Find The Common Difference In Sequences : Example Question #5
What is the common difference in this sequence?
−3,0,3,6,9,12,...
Possible Answers:
2
4
5
3
1
Correct answer:
3
Explanation:
The common difference is the distance between each number in the sequence. Notice that each number is 3 away from the previous number.
12−9=39−6=36−3=33−0=30−(−3)=3
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Find The Common Difference In Sequences : Example Question #6
What is the common difference in the following sequence?
3,11,19,27,35
Possible Answers:
16
4
19
8
Correct answer:
8
Explanation:
What is the common difference in the following sequence?
3,11,19,27,35
Common differences are associated with arithematic sequences.
A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third,
Answers & Comments
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Answer:
Which of the following cannot be three consecutive terms of an arithmetic sequence?
Possible Answers:
23,45,69
23,44,65
33,55,77
54,32,10
18,30,42
Correct answer:
23,45,69
Explanation:
In each group of numbers, compare the difference of the second and first terms to that of the third and second terms. The group in which they are unequal is the correct choice.
54,32,10:32−54=−22=10−32
23,44,65:44−23=21=65−44
33,55,77:55−33=22=77−55
18,30,42:30−18=12=42−30
23,45,69:45−23=22≠24=69−45
The last group of numbers is the correct choice.
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Find The Common Difference In Sequences : Example Question #2
Consider the arithmetic sequence
{2n+4,n2−3,6n,9n−7,9n+1}.
If n=5, find the common difference between consecutive terms.
Possible Answers:
−7
1
12
4
8
Correct answer:
8
Explanation:
In arithmetic sequences, the common difference is simply the value that is added to each term to produce the next term of the sequence. When solving this equation, one approach involves substituting 5 for n to find the numbers that make up this sequence. For example,
2(5)+4=14
so 14 is the first term of the sequence. However, a much easier approach involves only the last two terms, 9n−7 and 9n+1.
The difference between these expressions is 8, so this must be the common difference between consecutive terms in the sequence.
Report an Error
Find The Common Difference In Sequences : Example Question #3
Find the common difference in the following arithmetic sequence.
{16,32,48,64...}
Possible Answers:
32
0
16
2
4
Correct answer:
16
Explanation:
An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.
32−16=16
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Find The Common Difference In Sequences : Example Question #4
Find the common difference in the following arithmetic sequence.
{54,27,0,−27...}
Possible Answers:
−1
0
−27
−54
27
Correct answer:
−27
Explanation:
An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.
27−54=−27
(i.e. the sequence advances by subtracting 27)
Report an Error
Find The Common Difference In Sequences : Example Question #5
What is the common difference in this sequence?
−3,0,3,6,9,12,...
Possible Answers:
2
4
5
3
1
Correct answer:
3
Explanation:
The common difference is the distance between each number in the sequence. Notice that each number is 3 away from the previous number.
12−9=39−6=36−3=33−0=30−(−3)=3
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Find The Common Difference In Sequences : Example Question #6
What is the common difference in the following sequence?
3,11,19,27,35
Possible Answers:
16
4
19
8
Correct answer:
8
Explanation:
What is the common difference in the following sequence?
3,11,19,27,35
Common differences are associated with arithematic sequences.
A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third,
Step-by-step explanation:
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