Year 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 13 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & SeriesYear 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 29 terms of the arithmetic sequence 15, 11, 7, 3, …
Answer: −1189
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 15 + 28 × −4)
- = −1189
2.For the arithmetic sequence −4, 3, 10, 17, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 11
- d = 3 − (−4) = 7
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 7 = 7n − 11
3.Find the 6th term of the geometric sequence −5, 10, −20, 40, …
Answer: 160
- a = −5, r = −2
- T6 = −5 × (−2)5 = 160
4.Find the 28th term of the arithmetic sequence 1, 9, 17, 25, …
Answer: 217
- a = 1, d = 8
- T28 = 1 + 27 × 8 = 217
5.Find the 23th term of the arithmetic sequence −5, −10, −15, −20, …
Answer: −115
- a = −5, d = −5
- T23 = −5 + 22 × −5 = −115
6.For the geometric sequence −1, −5, −25, −125, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −1 × 5n − 1
- r = −5 ÷ (−1) = 5
7.Find the 6th term of the geometric sequence 3, 6, 12, 24, …
Answer: 96
- a = 3, r = 2
- T6 = 3 × 25 = 96
8.Find the sum of the first 6 terms of the geometric sequence −2, 4, −8, 16, …
Answer: 42
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × ((−2)6 − 1) ÷ (−2 − 1)
- = 42
9.Find the sum of the first 12 terms of the arithmetic sequence −7, −2, 3, 8, …
Answer: 246
- Sₙ = n/2 × (2a + (n − 1)d)
- = 12/2 × (2 × −7 + 11 × 5)
- = 246
10.Find the sum of the first 16 terms of the arithmetic sequence 10, 8, 6, 4, …
Answer: −80
- Sₙ = n/2 × (2a + (n − 1)d)
- = 16/2 × (2 × 10 + 15 × −2)
- = −80
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.
Great work. Here's what to try next: