Activity 1

Fill in the numbers that are missing in each sequence. Identify the rule that was used in the sequence.

1. [tex]$16, 20, 24, 28, 32, 36, 40, 44$[/tex]
- The rule for this sequence is:

2. [tex]$9, 5, 1, -3, -7, -11$[/tex]
- The rule for this sequence is:

3. [tex]$20, 30, 40, 50, 60, 70$[/tex]
- The rule for this sequence is:

4. [tex]$15, -45, -135, 405, -1215, 3645$[/tex]
- The rule for this sequence is:

5. [tex]$\frac{1}{3}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}$[/tex]
- The rule for this sequence is:



Answer :

Certainly! Let's work through each sequence in detail, identify the missing numbers, and state the rule for each sequence:

1. Sequence: [tex]\( 16, 20, 24, 28, 32, 36, 40, 44 \)[/tex]

Rule: This sequence increases by 4 with each step. The rule can be expressed as:
[tex]\[ a_n = 16 + 4n \][/tex]

This is an arithmetic sequence with a common difference of 4 starting at 16.

2. Sequence: [tex]\( 9, 5, 1, -3, -7, -11 \)[/tex]

Rule: This sequence decreases by 4 with each step. The rule can be expressed as:
[tex]\[ a_n = 9 - 4n \][/tex]

This is an arithmetic sequence with a common difference of -4 starting at 9.

3. Sequence: [tex]\( 20, 30, 40, \_, 60, 70 \)[/tex]

Rule: This sequence increases by 10 with each step. The rule can be expressed as:
[tex]\[ a_n = 20 + 10n \][/tex]

The missing number is 50. This is an arithmetic sequence with a common difference of 10 starting at 20.

4. Sequence: [tex]\( 15, -45, -135, \_, 1215, -3645 \)[/tex]

Rule: This sequence is geometric with each term being multiplied by -3. The rule can be expressed as:
[tex]\[ a_n = 15 \times (-3)^n \][/tex]

The missing number is [tex]\( 405 \)[/tex]. This is a geometric sequence where the ratio between terms is -3.

5. Sequence: [tex]\( \frac{1}{3}, \frac{1}{8}, \frac{1}{22}, \frac{1}{26} \)[/tex]

Rule: This sequence appears to follow the pattern:
[tex]\[ a_n = \frac{1}{4n - 1} \][/tex]

This is a sequence where the denominator increases in a specific arithmetic pattern.

So, filling in the missing details and rules, we have:

1. Sequence: [tex]\( 16, 20, 24, 28, 32, 36, 40, 44 \)[/tex]
Rule: [tex]\( a_n = 16 + 4n \)[/tex]

2. Sequence: [tex]\( 9, 5, 1, -3, -7, -11 \)[/tex]
Rule: [tex]\( a_n = 9 - 4n \)[/tex]

3. Sequence: [tex]\( 20, 30, 40, 50, 60, 70 \)[/tex]
Rule: [tex]\( a_n = 20 + 10n \)[/tex]

4. Sequence: [tex]\( 15, -45, -135, 405, -1215 \)[/tex]
Rule: [tex]\( a_n = 15 \times (-3)^n \)[/tex]

5. Sequence: [tex]\( \frac{1}{3}, \frac{1}{8}, \frac{1}{22}, \frac{1}{26} \)[/tex]
Rule: [tex]\( a_n = \frac{1}{4n - 1} \)[/tex]