Answered: Each gives the first term or two of a…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.2: Sequences, Series And Summation Notation

Problem 42E

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Question

Each gives the first term or two of a sequence along
with a recursion formula for the remaining terms. Write out the first
ten terms of the sequence. a1 = 1, an+1 = an/(n + 1)

Expert Solution

Step 1

Given:

$a_{1} = 1, a_{n + 1} = \frac{a_{n}}{n + 1}$ .

We have to write the first ten terms of the given sequence.

Step 2

First term:
$a_{1} = 1$

Second term:
$a_{2} = a_{1 + 1} = \frac{a_{1}}{1 + 1} = \frac{1}{2} a_{2} = \frac{1}{2}$

Third term:
$a_{3} = a_{2 + 1} = \frac{a_{2}}{2 + 1} = \frac{\frac{1}{2}}{3} = \frac{1}{6} a_{3} = \frac{1}{6}$

Fourth term:
$a_{4} = a_{3 + 1} = \frac{a_{3}}{3 + 1} = \frac{\frac{1}{6}}{4} = \frac{1}{24} a_{4} = \frac{1}{24}$

Fifth term:
$a_{5} = a_{4 + 1} = \frac{a_{4}}{4 + 1} = \frac{\frac{1}{24}}{5} = \frac{1}{120} a_{5} = \frac{1}{120}$

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