How to find the common difference in sequences - ACT Math
Card 0 of 5
In the sequence 3, ____, ____, 24, what numbers can fill the two blanks so that consecutive terms differ by a common ratio?
In the sequence 3, ____, ____, 24, what numbers can fill the two blanks so that consecutive terms differ by a common ratio?
If the common ratio is r, then the sequence can be rewritten as 3, 3r, , . We see then that , which gives us that r=2. Therefore, the missing terms are 6 and 12.
If the common ratio is r, then the sequence can be rewritten as 3, 3r, , . We see then that , which gives us that r=2. Therefore, the missing terms are 6 and 12.
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The following is an arithmetic sequence. Find an explicit equation for it in terms of the common difference.
The following is an arithmetic sequence. Find an explicit equation for it in terms of the common difference.
Finding the common difference is fairly simple. We simply subtract the first term from the second. 7-3 = 4, so 4 is our common difference. So each term is going to be 4n plus something:
We know the first term is 3, so we can plug in that to our equation.
So the explicit form of our arithmetic sequence is
.
Finding the common difference is fairly simple. We simply subtract the first term from the second. 7-3 = 4, so 4 is our common difference. So each term is going to be 4n plus something:
We know the first term is 3, so we can plug in that to our equation.
So the explicit form of our arithmetic sequence is
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Find the common difference of the following sequence:
Find the common difference of the following sequence:
The common difference is equal to
Plugging our values into this equation we can find the common difference.
Therefore, in this case the common difference is 
.
The common difference is equal to
Plugging our values into this equation we can find the common difference.
Therefore, in this case the common difference is
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Find the common difference of the following sequence:
Find the common difference of the following sequence:
The common difference is equal to
.
Plugging in the values from this problem we get,
Therefore, in this case the common difference is 
.
The common difference is equal to
Plugging in the values from this problem we get,
Therefore, in this case the common difference is
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Find the common difference of the following sequence:
Find the common difference of the following sequence:
The common difference is equal to
.
Plugging in the values from this problem we get,
Therefore, in this case the common difference is 
.
The common difference is equal to
Plugging in the values from this problem we get,
Therefore, in this case the common difference is
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