11th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence −4, −8, −16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −4 × 2n − 1
- r = −8 ÷ (−4) = 2
2.Find the 16th term of the arithmetic sequence −10, −12, −14, −16, …
Answer: −40
- a = −10, d = −2
- T16 = −10 + 15 × −2 = −40
3.Find the 19th term of the arithmetic sequence 10, 15, 20, 25, …
Answer: 100
- a = 10, d = 5
- T19 = 10 + 18 × 5 = 100
4.Find the 9th term of the geometric sequence 5, −10, 20, −40, …
Answer: 1280
- a = 5, r = −2
- T9 = 5 × (−2)8 = 1280
5.Find the sum of the first 7 terms of the geometric sequence 7, 21, 63, 189, …
Answer: 7651
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × (37 − 1) ÷ (3 − 1)
- = 7651
6.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
7.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
8.For the arithmetic sequence 4, 7, 10, 13, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 1
- d = 7 − 4 = 3
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 3 = 3n + 1
9.Find the 5th term of the geometric sequence 4, 8, 16, 32, …
Answer: 64
- a = 4, r = 2
- T5 = 4 × 24 = 64
10.Find the sum of the first 22 terms of the arithmetic sequence 7, 1, −5, −11, …
Answer: −1232
- Sₙ = n/2 × (2a + (n − 1)d)
- = 22/2 × (2 × 7 + 21 × −6)
- = −1232
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