Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$

The first five terms of the recursively defined sequence are $- 1, 1, 2, 9, and 47$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information.

The given recursively defined sequence is:

$a_{1} = - 1 a_{2} = 1 a_{n} = a_{n - 2} + n a_{n - 1}$

Step 2. Determine the first and second terms and find out the third term.

The first term is $(a_{1}) = - 1$ .

The second term islocalid="1646734892458" $(a_{2}) = 1$

Now substitute 3 for n in the given formula $a_{n} = a_{n - 2} + n a_{n - 1}$ to get the third term,

$a_{3} = a_{3 - 2} + 3 a_{3 - 1} = a_{1} + 3 a_{2} = (- 1) + 3 (1) = 2$

Step 3. Find the 4th and 5th terms.

Similarly substitute 4 and 5 for n in the given formula to get the fourth and fifth term,

$a_{4} = a_{4 - 2} + 4 a_{4 - 1} = a_{2} + 4 a_{3} = 1 + 4 (2) = 9 a_{5} = a_{5 - 2} + 5 a_{5 - 1} = a_{3} + 5 a_{4} = 2 + 5 (9) = 47$

Therefore, the first five terms are $- 1, 1, 2, 9, 47$ .

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$

Step by Step Solution

Step 1. Write the given information.

Step 2. Determine the first and second terms and find out the third term.

Step 3. Find the 4th and 5th terms.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.a1=-1; a2=1; an=an-2+nan-1

Step by Step Solution

Step 1. Write the given information.

Step 2. Determine the first and second terms and find out the third term.

Step 3. Find the 4th and 5th terms.

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In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$