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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 80. (page 809)

In Problems 71-82, find the sum of each sequence.
${鈭�}_{k = 8}^{40} (- 3 k)$

Short Answer

Expert verified

The sum of this sequence is -2376.

Step by step solution

01

Step 1. Write the given information.

The sum of sequence:

${鈭�}_{k = 8}^{40} (- 3 k)$

02

Step 2. Use the property of sequences.

Using the property of sequences: ${鈭� (c a_{k})}_{k = 1}^{n} = c {鈭� a_{k}}_{k = 1}^{n} S o, {鈭� (- 3 k)}_{k = 1}^{n} = - 3 {鈭� k}_{k = 1}^{n}$

03

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

${鈭� k}_{k = 8}^{40} = {鈭� k}_{k = 1}^{40} {- 鈭� k}_{k = 1}^{7} 鈬� {鈭� k}_{k = 8}^{40} = \frac{40 (40 + 1)}{2} - \frac{7 (7 + 1)}{2} 鈬� {鈭� k}_{k = 8}^{40} = 20 脳 41 - 7 脳 4 鈬� {鈭� k}_{k = 8}^{40} = 820 - 28 鈬� {鈭� k}_{k = 8}^{40} = 792$

04

Step 4. Use the property of sequences from Step 2.

Using the property of sequences gives:

${鈭� k}_{k = 8}^{40} = 792 鈬� (- {3) 鈭� k}_{k = 8}^{40} = - 3 脳 792 鈬� {(- 3) 鈭� k}_{k = 8}^{40} = - 2376$

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Most popular questions from this chapter

In Problems 11鈥�16, evaluate each factorial expression.

$\frac{9!}{6!}$

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 1; a_{2} = 2; a_{n} = a_{n - 1} 路 a_{n - 2}$

In Problems 71鈥�82, find the sum of each sequence.

${鈭�}_{k = 1}^{40} 5$

In Problems 51鈥�60, write out each sum.

${鈭�}_{k = 1}^{n} (k + 2)$

In Problems 51鈥�60, write out each sum.

${鈭�}_{k = 1}^{n} (2 k + 1)$

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