Let's solve each sequence one by one, determining whether it’s
Arithmetic or
Geometric, then find the
common difference (for arithmetic) or
common ratio (for geometric), and finally compute the
next two terms.
---
1) 14, 21, 28, 35, ...
Check differences:
- 21 - 14 =
7
- 28 - 21 =
7
- 35 - 28 =
7
✔ Constant difference →
Arithmetic Sequence
Common difference = 7
Next two terms:
- 35 + 7 =
42
- 42 + 7 =
49
✔ Answer:
- Arithmetic
- d = 7
- Next two terms:
42, 49
---
2) –1, 6, –36, 216, ...
Check ratios:
- 6 ÷ (–1) =
–6
- –36 ÷ 6 =
–6
- 216 ÷ (–36) =
–6
✔ Constant ratio →
Geometric Sequence
Common ratio = –6
Next two terms:
- 216 × (–6) =
–1296
- –1296 × (–6) =
7776
✔ Answer:
- Geometric
- r = –6
- Next two terms:
–1296, 7776
---
3) –1, –5, –25, –125, ...
Check ratios:
- –5 ÷ (–1) =
5
- –25 ÷ (–5) =
5
- –125 ÷ (–25) =
5
✔ Constant ratio →
Geometric Sequence
Common ratio = 5
Next two terms:
- –125 × 5 =
–625
- –625 × 5 =
–3125
✔ Answer:
- Geometric
- r = 5
- Next two terms:
–625, –3125
---
4) 8, 2, –4, –10, ...
Check differences:
- 2 – 8 =
–6
- –4 – 2 =
–6
- –10 – (–4) =
–6
✔ Constant difference →
Arithmetic Sequence
Common difference = –6
Next two terms:
- –10 + (–6) =
–16
- –16 + (–6) =
–22
✔ Answer:
- Arithmetic
- d = –6
- Next two terms:
–16, –22
---
5) 512, 128, 32, ...
Check ratios:
- 128 ÷ 512 =
1/4
- 32 ÷ 128 =
1/4
✔ Constant ratio →
Geometric Sequence
Common ratio = 1/4
Next two terms:
- 32 × (1/4) =
8
- 8 × (1/4) =
2
✔ Answer:
- Geometric
- r = 1/4
- Next two terms:
8, 2
---
##
✔ Final Answers Summary:
| Given Sequence | Arithmetic/Geometric | Common difference/ratio | Next two terms |
|------------------------|----------------------|--------------------------|--------------------|
| 1) 14, 21, 28, 35, ... | Arithmetic | d = 7 | 42, 49 |
| 2) –1, 6, –36, 216, ...| Geometric | r = –6 | –1296, 7776 |
| 3) –1, –5, –25, –125,..| Geometric | r = 5 | –625, –3125 |
| 4) 8, 2, –4, –10, ... | Arithmetic | d = –6 | –16, –22 |
| 5) 512, 128, 32, ... | Geometric | r = 1/4 | 8, 2 |
---
📌
Key Concepts Recap:
-
Arithmetic Sequence: Each term is obtained by adding a constant (
common difference) to the previous term.
-
Geometric Sequence: Each term is obtained by multiplying the previous term by a constant (
common ratio).
You can now fill in your worksheet with these answers! 😊
Parent Tip: Review the logic above to help your child master the concept of arithmetic and geometric sequence worksheet.
