11th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 6th term of the geometric sequence 5, 10, 20, 40, …
Answer: 160
- a = 5, r = 2
- T6 = 5 × 25 = 160
2.Find the 12th term of the arithmetic sequence 19, 17, 15, 13, …
Answer: −3
- a = 19, d = −2
- T12 = 19 + 11 × −2 = −3
3.Find the sum of the first 6 terms of the geometric sequence 1, 3, 9, 27, …
Answer: 364
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (36 − 1) ÷ (3 − 1)
- = 364
4.Find the 6th term of the geometric sequence 6, −12, 24, −48, …
Answer: −192
- a = 6, r = −2
- T6 = 6 × (−2)5 = −192
5.Find the 5th term of the geometric sequence 6, 12, 24, 48, …
Answer: 96
- a = 6, r = 2
- T5 = 6 × 24 = 96
6.Find the 7th term of the geometric sequence −5, −15, −45, −135, …
Answer: −3645
- a = −5, r = 3
- T7 = −5 × 36 = −3645
7.For the geometric sequence −5, −10, −20, −40, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −5 × 2n − 1
- r = −10 ÷ (−5) = 2
8.Find the sum of the first 6 terms of the geometric sequence −4, −16, −64, −256, …
Answer: −5460
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (46 − 1) ÷ (4 − 1)
- = −5460
9.For the arithmetic sequence −9, −11, −13, −15, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 7
- d = −11 − (−9) = −2
- Tₙ = a + (n − 1)d = −9 + (n − 1) × −2 = −2n − 7
10.Find the 18th term of the arithmetic sequence 2, 10, 18, 26, …
Answer: 138
- a = 2, d = 8
- T18 = 2 + 17 × 8 = 138
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