11th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 11th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Sequences & Series11th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 9th term of the arithmetic sequence −3, −8, −13, −18, …
Answer: −43
- a = −3, d = −5
- T9 = −3 + 8 × −5 = −43
2.For the geometric sequence 4, −8, 16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 4 × (−2)n − 1
- r = −8 ÷ 4 = −2
3.Find the sum of the first 9 terms of the geometric sequence 8, −16, 32, −64, …
Answer: 1368
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × ((−2)9 − 1) ÷ (−2 − 1)
- = 1368
4.Find the 9th term of the geometric sequence 8, −16, 32, −64, …
Answer: 2048
- a = 8, r = −2
- T9 = 8 × (−2)8 = 2048
5.Find the 5th term of the geometric sequence 4, −8, 16, −32, …
Answer: 64
- a = 4, r = −2
- T5 = 4 × (−2)4 = 64
6.Find the 6th term of the geometric sequence 6, 12, 24, 48, …
Answer: 192
- a = 6, r = 2
- T6 = 6 × 25 = 192
7.For the arithmetic sequence 7, 1, −5, −11, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 13
- d = 1 − 7 = −6
- Tₙ = a + (n − 1)d = 7 + (n − 1) × −6 = −6n + 13
8.Find the sum of the first 6 terms of the geometric sequence 3, −6, 12, −24, …
Answer: −63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × ((−2)6 − 1) ÷ (−2 − 1)
- = −63
9.Find the sum of the first 18 terms of the arithmetic sequence −3, −9, −15, −21, …
Answer: −972
- Sₙ = n/2 × (2a + (n − 1)d)
- = 18/2 × (2 × −3 + 17 × −6)
- = −972
10.Find the 8th term of the geometric sequence −5, −15, −45, −135, …
Answer: −10935
- a = −5, r = 3
- T8 = −5 × 37 = −10935
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