Q 76. In Problems 71-82, find the sum ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 76. (page 809)

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

Short Answer

Expert verified

The sum of this sequence is 871.

Step by step solution

Step 1. Write the given information.

The sum of sequence:

${鈭� (3 k - 7)}_{k = 1}^{26}$

Step 2. Use the properties of sequence.

Using the properties of sequence:

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

So,

${鈭� (3 k - 7)}_{k = 1}^{26} = {鈭� (3 k)}_{k = 1}^{26} - {鈭� (7)}_{k = 1}^{26}$

${鈭� (3 k)}_{k = 1}^{26} = {3 鈭� (k)}_{k = 1}^{26}$

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

Using formula for summation is:

${鈭� k}_{k = 1}^{n} = 1 + 2 + . . . + n 鈬� {鈭� k}_{k = 1}^{n} = \frac{n (n + 1)}{2}$

So,

role="math" localid="1646750162806" $3 {鈭� k}_{k = 1}^{26} = 3 脳 \frac{26 (26 + 1)}{2} 鈬� {3 鈭� k}_{k = 1}^{26} = 3 脳 \frac{26 (27)}{2} 鈬� {3 鈭� k}_{k = 1}^{26} = 3 脳 351 鈬� {3 鈭� k}_{k = 1}^{26} = 1053$

Step 4. Use the formula for sum of sequence.

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

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

From Step 3,

${3 鈭� k}_{k = 1}^{26} = 1053$

From Step 4,

${鈭� 7}_{k = 1}^{26} = 182$

So,

${鈭� (3 k - 7)}_{k = 1}^{26} = {鈭� (3 k)}_{k = 1}^{26} {- 鈭� (3)}_{k = 1}^{26} 鈬� {鈭� (3 k - 7)}_{k = 1}^{26} = 1053 - 182 鈬� {鈭� (3 k - 7)}_{k = 1}^{26} = 871$

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91影视

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

Short Answer

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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91影视

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

Short Answer

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.

One App. One Place for Learning.

Most popular questions from this chapter

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Calculus

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Study anywhere. Anytime. Across all devices.

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