Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 13th term of the arithmetic sequence 19, 16, 13, 10, …
Answer: −17
- a = 19, d = −3
- T13 = 19 + 12 × −3 = −17
2.Find the sum of the first 21 terms of the arithmetic sequence −10, −9, −8, −7, …
Answer: 0
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × −10 + 20 × 1)
- = 0
3.For the arithmetic sequence −7, −5, −3, −1, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 9
- d = −5 − (−7) = 2
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 2 = 2n − 9
4.Find the sum of the first 5 terms of the geometric sequence −3, −9, −27, −81, …
Answer: −363
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (35 − 1) ÷ (3 − 1)
- = −363
5.Find the sum of the first 5 terms of the geometric sequence −1, −5, −25, −125, …
Answer: −781
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (55 − 1) ÷ (5 − 1)
- = −781
6.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
7.For the arithmetic sequence −2, −7, −12, −17, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 3
- d = −7 − (−2) = −5
- Tₙ = a + (n − 1)d = −2 + (n − 1) × −5 = −5n + 3
8.Find the 5th term of the geometric sequence 3, 15, 75, 375, …
Answer: 1875
- a = 3, r = 5
- T5 = 3 × 54 = 1875
9.For the arithmetic sequence 10, 12, 14, 16, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 8
- d = 12 − 10 = 2
- Tₙ = a + (n − 1)d = 10 + (n − 1) × 2 = 2n + 8
10.For the arithmetic sequence 6, 12, 18, 24, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n
- d = 12 − 6 = 6
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 6 = 6n
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.
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