Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 7 terms of the geometric sequence −4, −8, −16, −32, …
Answer: −508
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (27 − 1) ÷ (2 − 1)
- = −508
2.For the arithmetic sequence 4, 9, 14, 19, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 1
- d = 9 − 4 = 5
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 5 = 5n − 1
3.Find the sum of the first 28 terms of the arithmetic sequence 8, 2, −4, −10, …
Answer: −2044
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × 8 + 27 × −6)
- = −2044
4.Find the 22th term of the arithmetic sequence 4, 11, 18, 25, …
Answer: 151
- a = 4, d = 7
- T22 = 4 + 21 × 7 = 151
5.Find the 6th term of the geometric sequence −3, −15, −75, −375, …
Answer: −9375
- a = −3, r = 5
- T6 = −3 × 55 = −9375
6.Find the sum of the first 7 terms of the geometric sequence 4, 12, 36, 108, …
Answer: 4372
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × (37 − 1) ÷ (3 − 1)
- = 4372
7.Find the sum of the first 6 terms of the geometric sequence −4, −12, −36, −108, …
Answer: −1456
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (36 − 1) ÷ (3 − 1)
- = −1456
8.Find the sum of the first 10 terms of the arithmetic sequence 1, −5, −11, −17, …
Answer: −260
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × 1 + 9 × −6)
- = −260
9.For the geometric sequence 7, −14, 28, −56, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 7 × (−2)n − 1
- r = −14 ÷ 7 = −2
10.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
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