Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 71-82, find the sum of each sequence.
${\sum (3}_{k = 1}^{26} k - 7)$

The sum of this sequence is 871.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information.

The sum of sequence:

${\sum (3 k - 7)}_{k = 1}^{26}$

Step 2. Use the properties of sequence.

Using the properties of sequence:

${\sum (a_{k} - b_{k})}_{k = 1}^{n} = {\sum (a_{k})}_{k = 1}^{n} - {\sum (b_{k})}_{k = 1}^{n} & {\sum (c a_{k})}_{k = 1}^{n} = c {\sum a_{k}}_{k = 1}^{n}$

So,

${\sum (3 k - 7)}_{k = 1}^{26} = {\sum (3 k)}_{k = 1}^{26} - {\sum (7)}_{k = 1}^{26}$

${\sum (3 k)}_{k = 1}^{26} = {3 \sum (k)}_{k = 1}^{26}$

Step 3. Use the formula for sum of sequences of n real numbers.

Using formula for summation is:

${\sum k}_{k = 1}^{n} = 1 + 2 + . . . + n \Rightarrow {\sum k}_{k = 1}^{n} = \frac{n (n + 1)}{2}$

So,

role="math" localid="1646750162806" $3 {\sum k}_{k = 1}^{26} = 3 \times \frac{26 (26 + 1)}{2} \Rightarrow {3 \sum k}_{k = 1}^{26} = 3 \times \frac{26 (27)}{2} \Rightarrow {3 \sum k}_{k = 1}^{26} = 3 \times 351 \Rightarrow {3 \sum k}_{k = 1}^{26} = 1053$

Step 4. Use the formula for sum of sequence.

Using formula for summation is: ${\sum c}_{k = 1}^{n} = c + c + . . . + c \Rightarrow {\sum c}_{k = 1}^{n} = c n, c - r e a l n u m b e r S o, {\sum 7}_{k = 1}^{26} = 7 \times 26 \Rightarrow {\sum 7}_{k = 1}^{26} = 182$

Step 5. Now, subtract Step 3 from Step 4.

From Step 3,

${3 \sum k}_{k = 1}^{26} = 1053$

From Step 4,

${\sum 7}_{k = 1}^{26} = 182$

So,

${\sum (3 k - 7)}_{k = 1}^{26} = {\sum (3 k)}_{k = 1}^{26} {- \sum (3)}_{k = 1}^{26} \Rightarrow {\sum (3 k - 7)}_{k = 1}^{26} = 1053 - 182 \Rightarrow {\sum (3 k - 7)}_{k = 1}^{26} = 871$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 71-82, find the sum of each sequence.
${\sum (3}_{k = 1}^{26} k - 7)$

Step by Step Solution

Step 1. Write the given information.

Step 2. Use the properties of sequence.

Step 3. Use the formula for sum of sequences of n real numbers.

Step 4. Use the formula for sum of sequence.

Step 5. Now, subtract Step 3 from Step 4.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 71-82, find the sum of each sequence.∑(3k=126k-7)

Step by Step Solution

Step 1. Write the given information.

Step 2. Use the properties of sequence.

Step 3. Use the formula for sum of sequences of n real numbers.

Step 4. Use the formula for sum of sequence.

Step 5. Now, subtract Step 3 from Step 4.

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In Problems 71-82, find the sum of each sequence.
${\sum (3}_{k = 1}^{26} k - 7)$