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.
$a_{1} = - 2; a_{n} = n + 3 a_{n - 1}$

The first five terms of the recursively defined sequence are $- 2, - 4, - 9, - 23, and - 64$ .

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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:

$a_{1} = - 2 a_{n} = n + 3 a_{n - 1}$

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

The first term is $(a_{1}) = 3$ .

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

role="math" localid="1646730495162" $a_{2} = 2 + 3 a_{2 - 1} = 2 + 3 a_{1} = 2 + 3 (- 2) = 2 - 6 = - 4$

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

Similarly substitute 3, 4 for n in the given formula to get the third and fourth term,

$a_{3} = 3 + 3 a_{3 - 1} = 3 + 3 a_{2} = 3 + 3 (- 4) = - 9 a_{4} = 4 + 3 a_{4 - 1} = 4 + 3 a_{3} = 4 + 3 (- 9) = 4 - 27 = - 23$

Step 4. Find the 5th term.

Now substitute 5 for n in the given formula to get the 5th term,

$a_{5} = 5 + 3 a_{5 - 1} = 5 + 3 a_{4} = 5 + 3 (- 23) = 5 - 69 = - 64$

Therefore, the first five terms are $- 2, - 4, - 9, - 23, - 64$ .

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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.
$a_{1} = - 2; a_{n} = n + 3 a_{n - 1}$

Step by Step Solution

Step 1. Write the given information.

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

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

Step 4. Find the 5th term.

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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=-2; an=n+3an-1

Step by Step Solution

Step 1. Write the given information.

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

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

Step 4. Find the 5th term.

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In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 2; a_{n} = n + 3 a_{n - 1}$