1). c
2). a
3). a **
4). d
5). a
6). c
** Question #3 has a typo (a typographical error, a misprint, an error, a mistake, a blunder, an oops, an owee) on the question sheet. The first number of the sequence should be 10,000 instead of 1000 .
1. If a sequence has a common ratio, it is called: C. Geometric Sequence
2. The sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. The common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. The sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. The next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
Recall:
1. Therefore, if a sequence has a common ratio, it is called: C. Geometric Sequence
2. Common ratio = next term / previous term
The sequence, -32, 16, -8, 4 has the following common ratio which is not -2:
[tex]\frac{4}{-8} = \frac{-8}{16} = \frac{16}{-32} = -\frac{1}{2}[/tex]
The common ratio is: [tex]-\frac{1}{2}[/tex]
Therefore, the sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. Find the common ratio of: 10,000, 1,000, 100, 10, 1
Common ratio = next term / previous term
Thus:
Common ratio = [tex]\frac{1}{10} = \frac{10}{100} = \frac{100}{1,000} = \frac{1,000}{10,000} = \frac{1}{10}[/tex]
Therefore, the common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. An arithmetic sequence is an ordered list whereby the next term is gotten by adding a constant to the previous term.
Simply put, the ordered list of numbers has a difference between each terms.
To find the common difference, subtract the previous term from the next term.
Thus:
-5, 0, 5, 10, 15 would have the following common difference:
0 - (-5) = 5
5 - 0 = 5
10 - 5 = 5
15 - 10 = 5
Also:
4, 1, -2, -5, -8 would have the following common difference:
1 - 4 = -3
-2 - 1 = -3
-5 -(-2) = -3
-8 -(-5) = -3
Therefore, the sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence, 5, -10, 20, -40, is a geometric sequence, that is it has a common ratio as shown below:
Common ratio = [tex]\frac{-40}{20} = \frac{20}{-10} = \frac{-10}{5} = -2[/tex]
The rest of the sequence in the answer choices have a common difference and are arithmetic sequences except 5, -10, 20, -40.
Therefore, the sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. To find the next term in the geometric sequence, [tex]\frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}[/tex], find the common ratio.
Then multiply it by the last term to get the next term in the sequence.
Common ratio = Next term / previous term
[tex]= \frac{1}{27} \div \frac{1}{9} \\\\= \frac{1}{27} \times \frac{9}{1} \\\\= \frac{1 \times 9}{27 \times 1}\\\\= \frac{9}{27} \\\\= \frac{1}{3}[/tex]
Multiply [tex]\frac{1}{3}[/tex] by [tex]\frac{1}{243}[/tex] to get the next term:
[tex]\frac{1}{243} \times \frac{1}{3} = \frac{1 \times 1}{243 \times 3} \\\\= \frac{1}{729}[/tex]
Therefore, the next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
In summary,
1. If a sequence has a common ratio, it is called: C. Geometric Sequence
2. The sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. The common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. The sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. The next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
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