How to find the common difference in sequences
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ACT Math › How to find the common difference in sequences
In the sequence 3, ____, ____, 24, what numbers can fill the two blanks so that consecutive terms differ by a common ratio?
6, 12
9, 18
10, 15
10, 17
12, 16
Explanation
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.
Find the common difference of the following sequence:
Explanation
The common difference is equal to
Plugging in the values from this problem we get,
Therefore, in this case the common difference is 
The following is an arithmetic sequence. Find an explicit equation for it in terms of the common difference.
Explanation
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
Find the common difference of the following sequence:
Explanation
The common difference is equal to
Plugging in the values from this problem we get,
Therefore, in this case the common difference is 
Find the common difference of the following sequence:
Explanation
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 