Answer :
Sure, let's create the sequences step by step according to the instructions.
### Part (a): Addition Sequence
1. Starting number: 4
2. Rule: Add 6 to the previous number to get the next number.
Let's calculate the sequence:
- Start with 4.
- Add 6 to 4 to get the next number: [tex]\( 4 + 6 = 10 \)[/tex]
- Add 6 to 10 to get the next number: [tex]\( 10 + 6 = 16 \)[/tex]
- Add 6 to 16 to get the next number: [tex]\( 16 + 6 = 22 \)[/tex]
- Add 6 to 22 to get the next number: [tex]\( 22 + 6 = 28 \)[/tex]
The first five numbers in this sequence are: 4, 10, 16, 22, 28.
### Part (b): Multiplication Sequence
1. Starting number: 4
2. Rule: Multiply the previous number by 3 to get the next number.
Let's calculate the sequence:
- Start with 4.
- Multiply 4 by 3 to get the next number: [tex]\( 4 \times 3 = 12 \)[/tex]
- Multiply 12 by 3 to get the next number: [tex]\( 12 \times 3 = 36 \)[/tex]
- Multiply 36 by 3 to get the next number: [tex]\( 36 \times 3 = 108 \)[/tex]
- Multiply 108 by 3 to get the next number: [tex]\( 108 \times 3 = 324 \)[/tex]
The first five numbers in this sequence are: 4, 12, 36, 108, 324.
### Part (a): Addition Sequence
1. Starting number: 4
2. Rule: Add 6 to the previous number to get the next number.
Let's calculate the sequence:
- Start with 4.
- Add 6 to 4 to get the next number: [tex]\( 4 + 6 = 10 \)[/tex]
- Add 6 to 10 to get the next number: [tex]\( 10 + 6 = 16 \)[/tex]
- Add 6 to 16 to get the next number: [tex]\( 16 + 6 = 22 \)[/tex]
- Add 6 to 22 to get the next number: [tex]\( 22 + 6 = 28 \)[/tex]
The first five numbers in this sequence are: 4, 10, 16, 22, 28.
### Part (b): Multiplication Sequence
1. Starting number: 4
2. Rule: Multiply the previous number by 3 to get the next number.
Let's calculate the sequence:
- Start with 4.
- Multiply 4 by 3 to get the next number: [tex]\( 4 \times 3 = 12 \)[/tex]
- Multiply 12 by 3 to get the next number: [tex]\( 12 \times 3 = 36 \)[/tex]
- Multiply 36 by 3 to get the next number: [tex]\( 36 \times 3 = 108 \)[/tex]
- Multiply 108 by 3 to get the next number: [tex]\( 108 \times 3 = 324 \)[/tex]
The first five numbers in this sequence are: 4, 12, 36, 108, 324.