High School Math Worksheets | Math Worksheets PDF - Free Printable

Let's solve each section of the worksheet "Generating Sequences" step by step. The goal is to generate terms of sequences using given formulas by substituting values of $ n = 1, 2, 3, \ldots $ into each expression.

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🔷 Section A: Find the first five terms of the following sequences.

We'll plug in $ n = 1 $ to $ n = 5 $ for each formula.

| $ n $ | $ n + 2 $ | $ n - 7 $ | $ 4n $ | $ 3n + 1 $ | $ 5n - 8 $ | $ 2n + 0.5 $ | $ 12n - 1.5 $ |
|--------|------------|------------|--------|-------------|--------------|----------------|------------------|
| 1 | 3 | -6 | 4 | 4 | -3 | 2.5 | 10.5 |
| 2 | 4 | -5 | 8 | 7 | 2 | 4.5 | 22.5 |
| 3 | 5 | -4 | 12 | 10 | 7 | 6.5 | 33.5 |
| 4 | 6 | -3 | 16 | 13 | 12 | 8.5 | 45.5 |
| 5 | 7 | -2 | 20 | 16 | 17 | 10.5 | 58.5 |

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🔷 Section B: Find the first five terms of the following sequences.

Again, substitute $ n = 1 $ to $ 5 $:

| $ n $ | $ 2 - n $ | $ 13 - n $ | $ -3n $ | $ 1 - 2n $ | $ -5n + 3 $ | $ \frac{1}{2}n $ | $ \frac{3}{4}n $ |
|--------|------------|-------------|---------|-------------|---------------|---------------------|---------------------|
| 1 | 1 | 12 | -3 | -1 | -2 | 0.5 | 0.75 |
| 2 | 0 | 11 | -6 | -3 | -7 | 1 | 1.5 |
| 3 | -1 | 10 | -9 | -5 | -12 | 1.5 | 2.25 |
| 4 | -2 | 9 | -12 | -7 | -17 | 2 | 3 |
| 5 | -3 | 8 | -15 | -9 | -22 | 2.5 | 3.75 |

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🔷 Section C: Find the first four terms of the following sequences.

Use $ n = 1 $ to $ 4 $.

1) $ 2n - 12 $
- $ n=1 $: $ 2(1) - 12 = -10 $
- $ n=2 $: $ 4 - 12 = -8 $
- $ n=3 $: $ 6 - 12 = -6 $
- $ n=4 $: $ 8 - 12 = -4 $
→ -10, -8, -6, -4

2) $ 6n - 10 $
- $ n=1 $: $ 6 - 10 = -4 $
- $ n=2 $: $ 12 - 10 = 2 $
- $ n=3 $: $ 18 - 10 = 8 $
- $ n=4 $: $ 24 - 10 = 14 $
→ -4, 2, 8, 14

3) $ n - 98 $
- $ n=1 $: $ 1 - 98 = -97 $
- $ n=2 $: $ 2 - 98 = -96 $
- $ n=3 $: $ 3 - 98 = -95 $
- $ n=4 $: $ 4 - 98 = -94 $
→ -97, -96, -95, -94

4) $ 3n + 7 $
- $ n=1 $: $ 3 + 7 = 10 $
- $ n=2 $: $ 6 + 7 = 13 $
- $ n=3 $: $ 9 + 7 = 16 $
- $ n=4 $: $ 12 + 7 = 19 $
→ 10, 13, 16, 19

5) $ 2.5n $
- $ n=1 $: $ 2.5 $
- $ n=2 $: $ 5 $
- $ n=3 $: $ 7.5 $
- $ n=4 $: $ 10 $
→ 2.5, 5, 7.5, 10

6) $ 4 - 2n $
- $ n=1 $: $ 4 - 2 = 2 $
- $ n=2 $: $ 4 - 4 = 0 $
- $ n=3 $: $ 4 - 6 = -2 $
- $ n=4 $: $ 4 - 8 = -4 $
→ 2, 0, -2, -4

7) $ 8 - n $
- $ n=1 $: $ 7 $
- $ n=2 $: $ 6 $
- $ n=3 $: $ 5 $
- $ n=4 $: $ 4 $
→ 7, 6, 5, 4

8) $ 0.5n + 3 $
- $ n=1 $: $ 0.5 + 3 = 3.5 $
- $ n=2 $: $ 1 + 3 = 4 $
- $ n=3 $: $ 1.5 + 3 = 4.5 $
- $ n=4 $: $ 2 + 3 = 5 $
→ 3.5, 4, 4.5, 5

9) $ 6 - 3n $
- $ n=1 $: $ 6 - 3 = 3 $
- $ n=2 $: $ 6 - 6 = 0 $
- $ n=3 $: $ 6 - 9 = -3 $
- $ n=4 $: $ 6 - 12 = -6 $
→ 3, 0, -3, -6

10) $ 6n $
- $ n=1 $: $ 6 $
- $ n=2 $: $ 12 $
- $ n=3 $: $ 18 $
- $ n=4 $: $ 24 $
→ 6, 12, 18, 24

11) $ \frac{n}{2} $
- $ n=1 $: $ 0.5 $
- $ n=2 $: $ 1 $
- $ n=3 $: $ 1.5 $
- $ n=4 $: $ 2 $
→ 0.5, 1, 1.5, 2

12) $ 8 - 5n $
- $ n=1 $: $ 8 - 5 = 3 $
- $ n=2 $: $ 8 - 10 = -2 $
- $ n=3 $: $ 8 - 15 = -7 $
- $ n=4 $: $ 8 - 20 = -12 $
→ 3, -2, -7, -12

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🔷 Section D (Level 7!): Find the first three terms of the following sequences.

Use $ n = 1, 2, 3 $

1) $ 2(n + 1) $
- $ n=1 $: $ 2(2) = 4 $
- $ n=2 $: $ 2(3) = 6 $
- $ n=3 $: $ 2(4) = 8 $
→ 4, 6, 8

2) $ n^2 $
- $ n=1 $: $ 1 $
- $ n=2 $: $ 4 $
- $ n=3 $: $ 9 $
→ 1, 4, 9

3) $ \frac{n+1}{n} $
- $ n=1 $: $ \frac{2}{1} = 2 $
- $ n=2 $: $ \frac{3}{2} = 1.5 $
- $ n=3 $: $ \frac{4}{3} \approx 1.333 $
→ 2, 1.5, 1.333...

4) $ 3(n + 5) $
- $ n=1 $: $ 3(6) = 18 $
- $ n=2 $: $ 3(7) = 21 $
- $ n=3 $: $ 3(8) = 24 $
→ 18, 21, 24

5) $ n^2 + 1 $
- $ n=1 $: $ 1 + 1 = 2 $
- $ n=2 $: $ 4 + 1 = 5 $
- $ n=3 $: $ 9 + 1 = 10 $
→ 2, 5, 10

6) $ \frac{3n}{2} $
- $ n=1 $: $ 1.5 $
- $ n=2 $: $ 3 $
- $ n=3 $: $ 4.5 $
→ 1.5, 3, 4.5

7) $ 10(n - 9) $
- $ n=1 $: $ 10(-8) = -80 $
- $ n=2 $: $ 10(-7) = -70 $
- $ n=3 $: $ 10(-6) = -60 $
→ -80, -70, -60

8) $ n^2 + 5 $
- $ n=1 $: $ 1 + 5 = 6 $
- $ n=2 $: $ 4 + 5 = 9 $
- $ n=3 $: $ 9 + 5 = 14 $
→ 6, 9, 14

9) $ n(n + 2) $
- $ n=1 $: $ 1(3) = 3 $
- $ n=2 $: $ 2(4) = 8 $
- $ n=3 $: $ 3(5) = 15 $
→ 3, 8, 15

10) $ 25(1 - n) $
- $ n=1 $: $ 25(0) = 0 $
- $ n=2 $: $ 25(-1) = -25 $
- $ n=3 $: $ 25(-2) = -50 $
→ 0, -25, -50

11) $ 2n^2 $
- $ n=1 $: $ 2(1) = 2 $
- $ n=2 $: $ 2(4) = 8 $
- $ n=3 $: $ 2(9) = 18 $
→ 2, 8, 18

12) $ n^3 $
- $ n=1 $: $ 1 $
- $ n=2 $: $ 8 $
- $ n=3 $: $ 27 $
→ 1, 8, 27

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✔ Final Answer Summary

All sections have been completed. Here’s a quick recap:

#### Section A & B: Tables filled with values for $ n = 1 $ to $ 5 $

#### Section C: First four terms:
1. -10, -8, -6, -4
2. -4, 2, 8, 14
3. -97, -96, -95, -94
4. 10, 13, 16, 19
5. 2.5, 5, 7.5, 10
6. 2, 0, -2, -4
7. 7, 6, 5, 4
8. 3.5, 4, 4.5, 5
9. 3, 0, -3, -6
10. 6, 12, 18, 24
11. 0.5, 1, 1.5, 2
12. 3, -2, -7, -12

#### Section D: First three terms:
1. 4, 6, 8
2. 1, 4, 9
3. 2, 1.5, 1.333...
4. 18, 21, 24
5. 2, 5, 10
6. 1.5, 3, 4.5
7. -80, -70, -60
8. 6, 9, 14
9. 3, 8, 15
10. 0, -25, -50
11. 2, 8, 18
12. 1, 8, 27

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✔ All problems solved! Let me know if you'd like this formatted as a printable answer key.