Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 26th term of the arithmetic sequence −5, −8, −11, −14, …
Answer: −80
- a = −5, d = −3
- T26 = −5 + 25 × −3 = −80
2.Find the sum of the first 15 terms of the arithmetic sequence −5, 1, 7, 13, …
Answer: 555
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × −5 + 14 × 6)
- = 555
3.Find the 5th term of the geometric sequence −2, 4, −8, 16, …
Answer: −32
- a = −2, r = −2
- T5 = −2 × (−2)4 = −32
4.For the geometric sequence −2, −4, −8, −16, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −2 × 2n − 1
- r = −4 ÷ (−2) = 2
5.Find the 5th term of the geometric sequence 8, −16, 32, −64, …
Answer: 128
- a = 8, r = −2
- T5 = 8 × (−2)4 = 128
6.Find the 13th term of the arithmetic sequence 20, 17, 14, 11, …
Answer: −16
- a = 20, d = −3
- T13 = 20 + 12 × −3 = −16
7.Find the 23th term of the arithmetic sequence −9, −10, −11, −12, …
Answer: −31
- a = −9, d = −1
- T23 = −9 + 22 × −1 = −31
8.Find the sum of the first 21 terms of the arithmetic sequence 5, 3, 1, −1, …
Answer: −315
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × 5 + 20 × −2)
- = −315
9.Find the 5th term of the geometric sequence −4, 8, −16, 32, …
Answer: −64
- a = −4, r = −2
- T5 = −4 × (−2)4 = −64
10.Find the 5th term of the geometric sequence 5, 10, 20, 40, …
Answer: 80
- a = 5, r = 2
- T5 = 5 × 24 = 80
Marking tips
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