Let’s go through each sequence one by one. We’ll check if it’s arithmetic (adding the same number each time) or geometric (multiplying by the same number each time). Then we’ll find the common difference or ratio, and finally calculate the next two terms.
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1) 14, 21, 28, 35, ...
Check differences:
- 21 - 14 = 7
- 28 - 21 = 7
- 35 - 28 = 7 → Same difference! So it’s
Arithmetic.
Common difference =
7
Next two terms:
- 35 + 7 =
42
- 42 + 7 =
49
✔ Answer for #1: Arithmetic, d=7, next terms: 42, 49
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2) –1, 6, –36, 216, ...
Check ratios (divide each term by previous):
- 6 ÷ (–1) = –6
- (–36) ÷ 6 = –6
- 216 ÷ (–36) = –6 → Same ratio! So it’s
Geometric.
Common ratio =
–6
Next two terms:
- 216 × (–6) =
–1296
- (–1296) × (–6) =
7776
✔ Answer for #2: Geometric, r=–6, next terms: –1296, 7776
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3) –1, –5, –25, –125, ...
Check ratios:
- (–5) ÷ (–1) = 5
- (–25) ÷ (–5) = 5
- (–125) ÷ (–25) = 5 → Same ratio! So it’s
Geometric.
Common ratio =
5
Next two terms:
- (–125) × 5 =
–625
- (–625) × 5 =
–3125
✔ Answer for #3: Geometric, r=5, next terms: –625, –3125
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4) 8, 2, –4, –10, ...
Check differences:
- 2 – 8 = –6
- (–4) – 2 = –6
- (–10) – (–4) = –6 → Same difference! So it’s
Arithmetic.
Common difference =
–6
Next two terms:
- (–10) + (–6) =
–16
- (–16) + (–6) =
–22
✔ Answer for #4: Arithmetic, d=–6, next terms: –16, –22
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5) 512, 128, 32, ...
Check ratios:
- 128 ÷ 512 = 0.25 → which is 1/4
- 32 ÷ 128 = 0.25 → also 1/4 → Same ratio! So it’s
Geometric.
Common ratio =
1/4 (or 0.25)
Next two terms:
- 32 × (1/4) =
8
- 8 × (1/4) =
2
✔ Answer for #5: Geometric, r=1/4, next terms: 8, 2
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Final Answer:
1) Arithmetic, common difference = 7, next two terms: 42, 49
2) Geometric, common ratio = –6, next two terms: –1296, 7776
3) Geometric, common ratio = 5, next two terms: –625, –3125
4) Arithmetic, common difference = –6, next two terms: –16, –22
5) Geometric, common ratio = 1/4, next two terms: 8, 2
Parent Tip: Review the logic above to help your child master the concept of arithmetic and geometric sequences worksheet.
