11th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the sum of the first 7 terms of the geometric sequence −1, 2, −4, 8, …
Answer: −43
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × ((−2)7 − 1) ÷ (−2 − 1)
- = −43
2.Find the 6th term of the geometric sequence −1, −5, −25, −125, …
Answer: −3125
- a = −1, r = 5
- T6 = −1 × 55 = −3125
3.Find the 7th term of the geometric sequence 8, 16, 32, 64, …
Answer: 512
- a = 8, r = 2
- T7 = 8 × 26 = 512
4.Find the 6th term of the geometric sequence −3, −9, −27, −81, …
Answer: −729
- a = −3, r = 3
- T6 = −3 × 35 = −729
5.Find the 5th term of the geometric sequence 6, 30, 150, 750, …
Answer: 3750
- a = 6, r = 5
- T5 = 6 × 54 = 3750
6.For the arithmetic sequence 14, 19, 24, 29, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 9
- d = 19 − 14 = 5
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 5 = 5n + 9
7.Find the sum of the first 9 terms of the geometric sequence −1, −3, −9, −27, …
Answer: −9841
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (39 − 1) ÷ (3 − 1)
- = −9841
8.Find the 5th term of the geometric sequence −1, 2, −4, 8, …
Answer: −16
- a = −1, r = −2
- T5 = −1 × (−2)4 = −16
9.Find the sum of the first 29 terms of the arithmetic sequence 4, 7, 10, 13, …
Answer: 1334
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 4 + 28 × 3)
- = 1334
10.Find the sum of the first 5 terms of the geometric sequence 8, 32, 128, 512, …
Answer: 2728
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (45 − 1) ÷ (4 − 1)
- = 2728
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