Find the number of items in the following sets. If there is an infinite number in a set enter oo (lower case o repeated 2 times). a) {2, 4, 6, ..., 22} has b) 10 20 30 11' 13' 17 has c) {7, 14, 21, ..., 63} has e) d) {-7, -14, -21,...} has 9 18 27 63 19' 19' 19 19 items. has items. items. items. items.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Instructions for Solving Set Problems**

Below are several sets. Your task is to find the number of items in each set. If a set contains an infinite number of items, indicate this by entering "oo" (lowercase letter 'o' repeated two times).

**Sets:**

a) \(\{2, 4, 6, \ldots, 22\}\) has [ ] items.

b) 
\[
\left\{
\frac{10}{11}, \frac{20}{13}, \frac{30}{17}, \ldots
\right\}
\]
has [ ] items.

c) \(\{7, 14, 21, \ldots, 63\}\) has [ ] items.

d) \(\{-7, -14, -21, \ldots\}\) has [ ] items.

e)
\[
\left\{
\frac{9}{19}, \frac{18}{19}, \frac{27}{19}, \ldots, \frac{63}{19}
\right\}
\]
has [ ] items.

**Explanation of Notations:**

1. **Ellipsis (\ldots):** This symbol indicates that the sequence continues in the same pattern.

2. **Set Notation (\{\}):** Curly braces are used to list the elements of a set.

3. **Fraction Notation (\frac{}{}):** Indicates the division of two numbers.

**Example of Analysis:**

- **Arithmetic Sequence:** If analyzing arithmetic sequences, identify the common difference between terms.

- **Infinite Series:** Consider the sequence pattern to determine if it continues indefinitely.

Apply these principles to determine the number of elements in each set.
Transcribed Image Text:**Instructions for Solving Set Problems** Below are several sets. Your task is to find the number of items in each set. If a set contains an infinite number of items, indicate this by entering "oo" (lowercase letter 'o' repeated two times). **Sets:** a) \(\{2, 4, 6, \ldots, 22\}\) has [ ] items. b) \[ \left\{ \frac{10}{11}, \frac{20}{13}, \frac{30}{17}, \ldots \right\} \] has [ ] items. c) \(\{7, 14, 21, \ldots, 63\}\) has [ ] items. d) \(\{-7, -14, -21, \ldots\}\) has [ ] items. e) \[ \left\{ \frac{9}{19}, \frac{18}{19}, \frac{27}{19}, \ldots, \frac{63}{19} \right\} \] has [ ] items. **Explanation of Notations:** 1. **Ellipsis (\ldots):** This symbol indicates that the sequence continues in the same pattern. 2. **Set Notation (\{\}):** Curly braces are used to list the elements of a set. 3. **Fraction Notation (\frac{}{}):** Indicates the division of two numbers. **Example of Analysis:** - **Arithmetic Sequence:** If analyzing arithmetic sequences, identify the common difference between terms. - **Infinite Series:** Consider the sequence pattern to determine if it continues indefinitely. Apply these principles to determine the number of elements in each set.
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Step 1: Find number of items in sequence of given sets a,b.

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