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Numerade Educator

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Problem 5 Easy Difficulty

List the first five terms of the sequence.
$ a_n = \frac {(-1)^{n-1}}{5^n} $

Answer

$\left\{\frac{1}{5},-\frac{1}{25}, \frac{1}{125},-\frac{1}{625}, \frac{1}{3125}, \dots\right\}$

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Video Transcript

first term. We're we're goingto have minus one to the one minus one. So minus one to the zero. Divided by five to the one. So anything that zero powers just one and five of the one is just five. So first term, it's one fifth. Next term we're looking at where plugging in n equals two. Now we're just gonna have minus one to the one divided by five. Squared A minus. I won over twenty five. Okay. And our terms should be alternating sign since we have minus one of the N minus one here. So this was positive. This was negative. Next term is going to be positive again. It'LL be minus one to the three minus one. So minus one squared, it will give us a positive number. Since his one over one hundred twenty five and drain equals four, you have minus one to the power of three. Which is the same thing is just minus one and we're dividing by five to four. So you can put that in a calculator in equals five. We should get a positive number since in equals. Forgive us a negative number, and this will be five to the five happening here. Okay, that's the first term. That's the second term. Third term for third, fifth time