Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Sequences & SeriesYear 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −6, −10, −14, −18, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n − 2
- d = −10 − (−6) = −4
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −4 = −4n − 2
2.Find the sum of the first 7 terms of the geometric sequence 5, 20, 80, 320, …
Answer: 27305
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (47 − 1) ÷ (4 − 1)
- = 27305
3.Find the 7th term of the geometric sequence −1, −4, −16, −64, …
Answer: −4096
- a = −1, r = 4
- T7 = −1 × 46 = −4096
4.Find the sum of the first 7 terms of the geometric sequence −3, 6, −12, 24, …
Answer: −129
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × ((−2)7 − 1) ÷ (−2 − 1)
- = −129
5.Find the sum of the first 7 terms of the geometric sequence 2, 4, 8, 16, …
Answer: 254
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (27 − 1) ÷ (2 − 1)
- = 254
6.Find the 13th term of the arithmetic sequence 1, 5, 9, 13, …
Answer: 49
- a = 1, d = 4
- T13 = 1 + 12 × 4 = 49
7.For the arithmetic sequence 6, 11, 16, 21, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 1
- d = 11 − 6 = 5
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 5 = 5n + 1
8.For the arithmetic sequence −1, −3, −5, −7, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 1
- d = −3 − (−1) = −2
- Tₙ = a + (n − 1)d = −1 + (n − 1) × −2 = −2n + 1
9.For the arithmetic sequence 0, −5, −10, −15, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 5
- d = −5 − 0 = −5
- Tₙ = a + (n − 1)d = 0 + (n − 1) × −5 = −5n + 5
10.Find the sum of the first 17 terms of the arithmetic sequence 5, 1, −3, −7, …
Answer: −459
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 5 + 16 × −4)
- = −459
Marking tips
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