11th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the sum of the first 30 terms of the arithmetic sequence −7, −13, −19, −25, …
Answer: −2820
- Sₙ = n/2 × (2a + (n − 1)d)
- = 30/2 × (2 × −7 + 29 × −6)
- = −2820
2.Find the 17th term of the arithmetic sequence 19, 21, 23, 25, …
Answer: 51
- a = 19, d = 2
- T17 = 19 + 16 × 2 = 51
3.Find the 9th term of the geometric sequence 5, 25, 125, 625, …
Answer: 1953125
- a = 5, r = 5
- T9 = 5 × 58 = 1953125
4.For the geometric sequence −3, −12, −48, −192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = −3 × 4n − 1
- r = −12 ÷ (−3) = 4
5.Find the 20th term of the arithmetic sequence 3, 4, 5, 6, …
Answer: 22
- a = 3, d = 1
- T20 = 3 + 19 × 1 = 22
6.Find the 14th term of the arithmetic sequence 0, −3, −6, −9, …
Answer: −39
- a = 0, d = −3
- T14 = 0 + 13 × −3 = −39
7.For the geometric sequence 3, −6, 12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 3 × (−2)n − 1
- r = −6 ÷ 3 = −2
8.Find the sum of the first 7 terms of the geometric sequence −4, −16, −64, −256, …
Answer: −21844
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (47 − 1) ÷ (4 − 1)
- = −21844
9.Find the 8th term of the geometric sequence 4, 12, 36, 108, …
Answer: 8748
- a = 4, r = 3
- T8 = 4 × 37 = 8748
10.Find the 7th term of the geometric sequence −4, 8, −16, 32, …
Answer: −256
- a = −4, r = −2
- T7 = −4 × (−2)6 = −256
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