Year 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 6, 12, 24, 48, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 6 × 2n − 1
- r = 12 ÷ 6 = 2
2.Find the 7th term of the geometric sequence −4, 8, −16, 32, …
Answer: −256
- a = −4, r = −2
- T7 = −4 × (−2)6 = −256
3.For the arithmetic sequence 17, 16, 15, 14, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 18
- d = 16 − 17 = −1
- Tₙ = a + (n − 1)d = 17 + (n − 1) × −1 = −n + 18
4.Find the sum of the first 6 terms of the geometric sequence 7, 21, 63, 189, …
Answer: 2548
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × (36 − 1) ÷ (3 − 1)
- = 2548
5.Find the 7th term of the geometric sequence 4, 16, 64, 256, …
Answer: 16384
- a = 4, r = 4
- T7 = 4 × 46 = 16384
6.Find the sum of the first 24 terms of the arithmetic sequence −5, 0, 5, 10, …
Answer: 1260
- Sₙ = n/2 × (2a + (n − 1)d)
- = 24/2 × (2 × −5 + 23 × 5)
- = 1260
7.Find the 6th term of the geometric sequence 8, 32, 128, 512, …
Answer: 8192
- a = 8, r = 4
- T6 = 8 × 45 = 8192
8.Find the sum of the first 6 terms of the geometric sequence −1, −4, −16, −64, …
Answer: −1365
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (46 − 1) ÷ (4 − 1)
- = −1365
9.Find the 23th term of the arithmetic sequence 11, 20, 29, 38, …
Answer: 209
- a = 11, d = 9
- T23 = 11 + 22 × 9 = 209
10.Find the 5th term of the geometric sequence 8, 40, 200, 1000, …
Answer: 5000
- a = 8, r = 5
- T5 = 8 × 54 = 5000
Marking tips
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