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.
${\sum (5}_{k = 1}^{20} k + 3)$

The sum of this sequence is 1110.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information.

The sum of sequence:

${\sum (5 k + 3)}_{k = 1}^{20}$

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,

${\sum (5 k + 3)}_{k = 1}^{20} = {\sum (5 k)}_{k = 1}^{20} + {\sum (3)}_{k = 1}^{20}$

${\sum (5 k)}_{k = 1}^{20} = {5 \sum (k)}_{k = 1}^{20}$

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,

$5 {\sum k}_{k = 1}^{20} = 5 \times \frac{20 (20 + 1)}{2} \Rightarrow {5 \sum k}_{k = 1}^{n} = 5 \times \frac{20 (21)}{2} \Rightarrow {5 \sum k}_{k = 1}^{n} = 5 \times 210 \Rightarrow {5 \sum k}_{k = 1}^{n} = 1050$

Step 4. Use the formula for sum of sequence.

Using formula for summation is:

${\sum c}_{k = 1}^{n} = c + c + . . . + c \Rightarrow {\sum c}_{k = 1}^{n} = c n, c - r e a l n u m b e r S o, {\sum 3}_{k = 1}^{20} = 3 \times 20 \Rightarrow {\sum 3}_{k = 1}^{20} = 60$

Step 5. Now, add the two sums from Step 3 and Step 4.

From Step 3,

${5 \sum k}_{k = 1}^{n} = 1050$

From Step 4,

${\sum 3}_{k = 1}^{20} = 60$

So,

localid="1646750229919" ${\sum (5 k + 3)}_{k = 1}^{20} = {\sum (5 k)}_{k = 1}^{20} + {\sum (3)}_{k = 1}^{20} \Rightarrow {\sum (5 k + 3)}_{k = 1}^{20} = 1050 + 60 \Rightarrow {\sum (5 k + 3)}_{k = 1}^{20} = 1110$

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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.
${\sum (5}_{k = 1}^{20} k + 3)$

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, add the two sums from Step 3 and 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.∑(5k=120k+3)

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, add the two sums from Step 3 and Step 4.

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In Problems 71-82, find the sum of each sequence.
${\sum (5}_{k = 1}^{20} k + 3)$