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Sequence:

1. [tex]\(6, 60, 600, 6000, 60000, \ldots\)[/tex]
2. [tex]\(100, 20, 4, 0.8, 0.16, \ldots\)[/tex]
3. [tex]\(2, 4, 8, 16, 32, 64, \ldots\)[/tex]
4. [tex]\(64, 96, 144, 216, 324, \ldots\)[/tex]
5. [tex]\(2, 6, 18, 54, 162, 486, \ldots\)[/tex]
6. [tex]\(25, 27.5, 30.25, 33.275, 36.6025, \ldots\)[/tex]

Pattern:

a. multiplying by [tex]\(\frac{1}{5}\)[/tex]
b. multiplying by 1.1
c. multiplying by 2
d. multiplying by 3
e. multiplying by 1.5
f. multiplying by 10

Answer :

Sure! Let's take a step-by-step approach to identify the pattern for each sequence and determine the operation used:

1. Sequence: [tex]\(6, 60, 600, 6000, 60000, \ldots\)[/tex]
- Pattern: Each term is multiplied by 10 to get the next term.
- Answer: Multiplying by 10.

2. Sequence: [tex]\(100, 20, 4, 0.8, 0.16, \ldots\)[/tex]
- Pattern: Each term is obtained by multiplying the previous term by [tex]\(\frac{1}{5}\)[/tex].
- Answer: Multiplying by [tex]\(\frac{1}{5}\)[/tex].

3. Sequence: [tex]\(2, 4, 8, 16, 32, 64, \ldots\)[/tex]
- Pattern: Each term is twice the previous term, which means multiplying by 2.
- Answer: Multiplying by 2.

4. Sequence: [tex]\(64, 96, 144, 216, 324, \ldots\)[/tex]
- Pattern: This sequence is obtained by multiplying each term by 1.5 to get the next term.
- Answer: Multiplying by 1.5.

5. Sequence: [tex]\(2, 6, 18, 54, 162, 486, \ldots\)[/tex]
- Pattern: Each term is obtained by multiplying the previous term by 3.
- Answer: Multiplying by 3.

6. Sequence: [tex]\(25, 27.5, 30.25, 33.275, 36.6025, \ldots\)[/tex]
- Pattern: Each term is multiplied by 1.1 to get the next term.
- Answer: Multiplying by 1.1.

So the patterns for the sequences are:
- Sequence 1: Multiplying by 10
- Sequence 2: Multiplying by [tex]\(\frac{1}{5}\)[/tex]
- Sequence 3: Multiplying by 2
- Sequence 4: Multiplying by 1.5
- Sequence 5: Multiplying by 3
- Sequence 6: Multiplying by 1.1

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