10th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 10th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Sequences & Series10th 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 sum of the first 8 terms of the arithmetic sequence −4, 5, 14, 23, …
Answer: 220
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × −4 + 7 × 9)
- = 220
2.Find the sum of the first 7 terms of the geometric sequence 8, 24, 72, 216, …
Answer: 8744
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (37 − 1) ÷ (3 − 1)
- = 8744
3.Find the sum of the first 5 terms of the geometric sequence −2, −10, −50, −250, …
Answer: −1562
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × (55 − 1) ÷ (5 − 1)
- = −1562
4.Find the sum of the first 7 terms of the geometric sequence −5, −15, −45, −135, …
Answer: −5465
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (37 − 1) ÷ (3 − 1)
- = −5465
5.For the arithmetic sequence 18, 22, 26, 30, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 14
- d = 22 − 18 = 4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 4 = 4n + 14
6.Find the sum of the first 8 terms of the arithmetic sequence 0, 9, 18, 27, …
Answer: 252
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × 0 + 7 × 9)
- = 252
7.Find the 17th term of the arithmetic sequence −10, −9, −8, −7, …
Answer: 6
- a = −10, d = 1
- T17 = −10 + 16 × 1 = 6
8.Find the 6th term of the geometric sequence 4, 8, 16, 32, …
Answer: 128
- a = 4, r = 2
- T6 = 4 × 25 = 128
9.Find the 5th term of the geometric sequence −2, −10, −50, −250, …
Answer: −1250
- a = −2, r = 5
- T5 = −2 × 54 = −1250
10.Find the 29th term of the arithmetic sequence 3, 9, 15, 21, …
Answer: 171
- a = 3, d = 6
- T29 = 3 + 28 × 6 = 171
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