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Numerade Educator

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Problem 11 Easy Difficulty

List the first five terms of the sequence.
$ a_1 = 2, a_{n+1} = \frac {a_n}{1 + a_n} $

Answer

$\left\{2, \frac{2}{3}, \frac{2}{5}, \frac{2}{7}, \frac{2}{5}, \dots,\right\}$

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Video Transcript

first term is given to us. They want us to. A two is a one over one plus one. So to over three Hey, through is a two over one, plus a two two thirds divided by one plus two thirds. And to simplify this, we can multiply the top on the bottom by three to get to over three plus two. Two over five four. It's a three over one, plus a three god, two over five, delighted by one plus two over five. And we can use the same type of trick to simplify. Here multiplied top and bottom by five. We get to delighted by five plus two to over seven and then a five. A four over one plus a four. A four was to over seven, and we simplify this by multiplying top bottom by seven. So we get to over seven plus two. So two overnight meccas us the first five terms in our sequence.