Matthew H. answered • 01/07/16
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an = 2 + (n - 1)9
Mark would have had the right answer to this question if you had asked "What IS the explicit formula..." but I think your real question is "HOW do you find it?" That way, no matter what the numbers are, the process is the same.
First you have to figure out what the common difference is. In this case, we already have it: 9. That means that somewhere in your formula, there will be a 9 because each term is 9 more than the previous one.
Next we need to figure out how to relate 9 to the first term of the series. An easy way to do this is to make (n-1) the term you multiply 9 by so that when you set n = 1, the output for the (n-1)9 part is 0. That means that in order to get an overall output of 2, you just have to add 2 to the (n-1)9 part we already found.
Thus, an = 2 + (n - 1)9 tells us that our first term will be 2 because
2 + (1-1)9 =
2 + (0)9 =
2
