10th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — 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 3 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 6th term of the geometric sequence 6, 12, 24, 48, …
Answer: 192
- a = 6, r = 2
- T6 = 6 × 25 = 192
2.For the arithmetic sequence 17, 23, 29, 35, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 11
- d = 23 − 17 = 6
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 6 = 6n + 11
3.Find the sum of the first 6 terms of the geometric sequence −4, −16, −64, −256, …
Answer: −5460
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (46 − 1) ÷ (4 − 1)
- = −5460
4.Find the 6th term of the geometric sequence 6, 30, 150, 750, …
Answer: 18750
- a = 6, r = 5
- T6 = 6 × 55 = 18750
5.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
6.Find the 30th term of the arithmetic sequence 11, 16, 21, 26, …
Answer: 156
- a = 11, d = 5
- T30 = 11 + 29 × 5 = 156
7.Find the sum of the first 9 terms of the geometric sequence −3, −9, −27, −81, …
Answer: −29523
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (39 − 1) ÷ (3 − 1)
- = −29523
8.For the geometric sequence −2, −4, −8, −16, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −2 × 2n − 1
- r = −4 ÷ (−2) = 2
9.Find the sum of the first 9 terms of the arithmetic sequence 9, 17, 25, 33, …
Answer: 369
- Sₙ = n/2 × (2a + (n − 1)d)
- = 9/2 × (2 × 9 + 8 × 8)
- = 369
10.Find the 28th term of the arithmetic sequence −7, −8, −9, −10, …
Answer: −34
- a = −7, d = −1
- T28 = −7 + 27 × −1 = −34
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.