First, lets find out how much each number goes up by in the sequence:
Lets subtract 4 from 11:
11 - 4 = 7
Lets do it again with another pair of numbers to make sure all of the numbers go up by 7:
18 - 11 = 7
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Now we know that the sequence goes up by 7 each time.
Next, lets compare the sequence to the 7 times table: (since sequence goes in 7's)
7 14 21 28 35 42 (7 times table)
4 11 18 25 32 39 (Sequence)
Lets see the difference between the 7 times table and the sequence.
We do this by subtracting on number from the sequence from the opposite number from the 7 times table.
Lets choose 7 and 4:
7 - 4 = 3 So the difference between the sequence and the 7 times table is 3
This means that we get the sequence by using the 7 times table minus 3: (7times table - 1)
Therefore the General Rule for the arithmetic sequence is:
7n - 3
(note: n stands for the term for a sequence. For example, 11 is the 2nd term in the sequence)
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Answer:
7n - 3