Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 5th term of the geometric sequence −1, −4, −16, −64, …
Answer: −256
- a = −1, r = 4
- T5 = −1 × 44 = −256
2.Find the 9th term of the geometric sequence 3, 12, 48, 192, …
Answer: 196608
- a = 3, r = 4
- T9 = 3 × 48 = 196608
3.For the arithmetic sequence −6, −8, −10, −12, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 4
- d = −8 − (−6) = −2
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −2 = −2n − 4
4.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
5.Find the sum of the first 8 terms of the geometric sequence 3, 15, 75, 375, …
Answer: 292968
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × (58 − 1) ÷ (5 − 1)
- = 292968
6.Find the 29th term of the arithmetic sequence 5, 3, 1, −1, …
Answer: −51
- a = 5, d = −2
- T29 = 5 + 28 × −2 = −51
7.Find the sum of the first 28 terms of the arithmetic sequence −5, −6, −7, −8, …
Answer: −518
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × −5 + 27 × −1)
- = −518
8.Find the 27th term of the arithmetic sequence −10, −2, 6, 14, …
Answer: 198
- a = −10, d = 8
- T27 = −10 + 26 × 8 = 198
9.For the arithmetic sequence 1, 0, −1, −2, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 2
- d = 0 − 1 = −1
- Tₙ = a + (n − 1)d = 1 + (n − 1) × −1 = −n + 2
10.Find the 7th term of the geometric sequence −5, 10, −20, 40, …
Answer: −320
- a = −5, r = −2
- T7 = −5 × (−2)6 = −320
Marking tips
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