11th Grade Arithmetic and Geometric Sequences Worksheet — Level 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence −3, −6, −12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −3 × 2n − 1
- r = −6 ÷ (−3) = 2
2.Find the 16th term of the arithmetic sequence −3, −1, 1, 3, …
Answer: 27
- a = −3, d = 2
- T16 = −3 + 15 × 2 = 27
3.Find the sum of the first 26 terms of the arithmetic sequence 20, 28, 36, 44, …
Answer: 3120
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 20 + 25 × 8)
- = 3120
4.Find the 5th term of the geometric sequence 5, 20, 80, 320, …
Answer: 1280
- a = 5, r = 4
- T5 = 5 × 44 = 1280
5.Find the 23th term of the arithmetic sequence 10, 14, 18, 22, …
Answer: 98
- a = 10, d = 4
- T23 = 10 + 22 × 4 = 98
6.Find the 5th term of the geometric sequence −5, −25, −125, −625, …
Answer: −3125
- a = −5, r = 5
- T5 = −5 × 54 = −3125
7.Find the 13th term of the arithmetic sequence 20, 24, 28, 32, …
Answer: 68
- a = 20, d = 4
- T13 = 20 + 12 × 4 = 68
8.Find the 19th term of the arithmetic sequence 0, 6, 12, 18, …
Answer: 108
- a = 0, d = 6
- T19 = 0 + 18 × 6 = 108
9.Find the sum of the first 5 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −2343
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (55 − 1) ÷ (5 − 1)
- = −2343
10.For the arithmetic sequence 18, 16, 14, 12, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 20
- d = 16 − 18 = −2
- Tₙ = a + (n − 1)d = 18 + (n − 1) × −2 = −2n + 20
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