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Find a formula for the general term $ a_n $ of the sequence, assuming that the pattern of the first few terms continues.$ \left\{\begin{array} \frac {1}{2}, \frac {1}{4}, \frac {1}{6}, \frac {1}{8}, \frac {1}{10}, . . . .\end{array}\right\} $
$\frac{1}{2 n}$
Calculus 2 / BC
Chapter 11
Infinite Sequences and Series
Section 1
Sequences
Series
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this first term is supposed to be at one half. Otherwise, it would not be very clear what this pattern wass. But assuming this first term is supposed to be one half, the pattern looks like it fairly clear. It's just the consecutive even numbers in the denominator, starting with two and one up top. Okay, so start with one half with two in the denominator, the next even numbers for next, even numbers. Six. And you can see those showing up in the denominators over here to the even. Numbers look like one over two in. So if we just write a N as one over two in, we see that that's going to get off the even numbers. And, you know, once you have a guest like this, you can plug in some values of end to really make sure that you have the correct thing. So a one, if we're correct, should be one half, and that's correct. And then you can check for any equals two. If you're still not sure that this is the correct formula
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