Certainly! Let's fill in the next five terms for each of the given sequences based on their rules.
[tex]\[
\begin{tabular}{|c|l|c|c|}
\hline & \multicolumn{1}{|c|}{ Rule } & First term & Next five terms \\
\hline a & add 4 & 3 & 7, 11, 15, 19, 23 \\
\hline b & subtract 9 & 60 & 51, 42, 33, 24, 15 \\
\hline c & multiply by 2 & 2 & 4, 8, 16, 32, 64 \\
\hline d & divide by 2 & 128 & 64.0, 32.0, 16.0, 8.0, 4.0 \\
\hline
\end{tabular}
\][/tex]
Let's break down how we determine these next five terms step-by-step.
### Sequence a: Add 4
Rule: Start at 3, add 4 each step.
1. Start: 3
2. 3 + 4 = 7
3. 7 + 4 = 11
4. 11 + 4 = 15
5. 15 + 4 = 19
6. 19 + 4 = 23
### Sequence b: Subtract 9
Rule: Start at 60, subtract 9 each step.
1. Start: 60
2. 60 - 9 = 51
3. 51 - 9 = 42
4. 42 - 9 = 33
5. 33 - 9 = 24
6. 24 - 9 = 15
### Sequence c: Multiply by 2
Rule: Start at 2, multiply by 2 each step.
1. Start: 2
2. 2 2 = 4
3. 4 2 = 8
4. 8 2 = 16
5. 16 2 = 32
6. 32 * 2 = 64
### Sequence d: Divide by 2
Rule: Start at 128, divide by 2 each step.
1. Start: 128
2. 128 / 2 = 64.0
3. 64.0 / 2 = 32.0
4. 32.0 / 2 = 16.0
5. 16.0 / 2 = 8.0
6. 8.0 / 2 = 4.0
By following these steps, we've filled in the next five terms for each sequence.
