Year 13 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence −5, −25, −125, −625, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −5 × 5n − 1
- r = −25 ÷ (−5) = 5
2.Find the sum of the first 9 terms of the geometric sequence −3, −9, −27, −81, …
Answer: −29523
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (39 − 1) ÷ (3 − 1)
- = −29523
3.Find the 5th term of the geometric sequence 7, 35, 175, 875, …
Answer: 4375
- a = 7, r = 5
- T5 = 7 × 54 = 4375
4.Find the sum of the first 17 terms of the arithmetic sequence 18, 12, 6, 0, …
Answer: −510
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 18 + 16 × −6)
- = −510
5.Find the 6th term of the geometric sequence 2, 4, 8, 16, …
Answer: 64
- a = 2, r = 2
- T6 = 2 × 25 = 64
6.Find the 28th term of the arithmetic sequence 8, 12, 16, 20, …
Answer: 116
- a = 8, d = 4
- T28 = 8 + 27 × 4 = 116
7.Find the 25th term of the arithmetic sequence 4, 6, 8, 10, …
Answer: 52
- a = 4, d = 2
- T25 = 4 + 24 × 2 = 52
8.For the arithmetic sequence 10, 4, −2, −8, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 16
- d = 4 − 10 = −6
- Tₙ = a + (n − 1)d = 10 + (n − 1) × −6 = −6n + 16
9.Find the sum of the first 25 terms of the arithmetic sequence 5, 9, 13, 17, …
Answer: 1325
- Sₙ = n/2 × (2a + (n − 1)d)
- = 25/2 × (2 × 5 + 24 × 4)
- = 1325
10.Find the sum of the first 7 terms of the geometric sequence −3, −6, −12, −24, …
Answer: −381
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (27 − 1) ÷ (2 − 1)
- = −381
Marking tips
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