Q 75. 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 75. (page 809)

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

Short Answer

Expert verified

The sum of this sequence is 1110.

Step by step solution

Step 1. Write the given information.

The sum of sequence:

${鈭� (5 k + 3)}_{k = 1}^{20}$

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,

${鈭� (5 k + 3)}_{k = 1}^{20} = {鈭� (5 k)}_{k = 1}^{20} + {鈭� (3)}_{k = 1}^{20}$

${鈭� (5 k)}_{k = 1}^{20} = {5 鈭� (k)}_{k = 1}^{20}$

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,

$5 {鈭� k}_{k = 1}^{20} = 5 脳 \frac{20 (20 + 1)}{2} 鈬� {5 鈭� k}_{k = 1}^{n} = 5 脳 \frac{20 (21)}{2} 鈬� {5 鈭� k}_{k = 1}^{n} = 5 脳 210 鈬� {5 鈭� k}_{k = 1}^{n} = 1050$

Step 4. Use the formula for sum of sequence.

Using formula for summation is:

${鈭� c}_{k = 1}^{n} = c + c + . . . + c 鈬� {鈭� c}_{k = 1}^{n} = c n, c - r e a l n u m b e r S o, {鈭� 3}_{k = 1}^{20} = 3 脳 20 鈬� {鈭� 3}_{k = 1}^{20} = 60$

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

From Step 3,

${5 鈭� k}_{k = 1}^{n} = 1050$

From Step 4,

${鈭� 3}_{k = 1}^{20} = 60$

So,

localid="1646750229919" ${鈭� (5 k + 3)}_{k = 1}^{20} = {鈭� (5 k)}_{k = 1}^{20} + {鈭� (3)}_{k = 1}^{20} 鈬� {鈭� (5 k + 3)}_{k = 1}^{20} = 1050 + 60 鈬� {鈭� (5 k + 3)}_{k = 1}^{20} = 1110$

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91影视

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

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

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91影视

In Problems 71-82, find the sum of each sequence.鈭�(5k=120k+3)

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

One App. One Place for Learning.

Most popular questions from this chapter

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