10th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 18th term of the arithmetic sequence 1, −1, −3, −5, …
Answer: −33
- a = 1, d = −2
- T18 = 1 + 17 × −2 = −33
2.For the arithmetic sequence 1, 9, 17, 25, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 7
- d = 9 − 1 = 8
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 8 = 8n − 7
3.Find the 9th term of the arithmetic sequence 16, 14, 12, 10, …
Answer: 0
- a = 16, d = −2
- T9 = 16 + 8 × −2 = 0
4.For the arithmetic sequence −4, 3, 10, 17, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 11
- d = 3 − (−4) = 7
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 7 = 7n − 11
5.For the arithmetic sequence 7, 3, −1, −5, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 11
- d = 3 − 7 = −4
- Tₙ = a + (n − 1)d = 7 + (n − 1) × −4 = −4n + 11
6.For the arithmetic sequence −3, −7, −11, −15, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 1
- d = −7 − (−3) = −4
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −4 = −4n + 1
7.For the arithmetic sequence 13, 16, 19, 22, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 10
- d = 16 − 13 = 3
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 3 = 3n + 10
8.Find the 10th term of the arithmetic sequence 1, 4, 7, 10, …
Answer: 28
- a = 1, d = 3
- T10 = 1 + 9 × 3 = 28
9.Find the 18th term of the arithmetic sequence 3, 1, −1, −3, …
Answer: −31
- a = 3, d = −2
- T18 = 3 + 17 × −2 = −31
10.Find the 30th term of the arithmetic sequence 2, −3, −8, −13, …
Answer: −143
- a = 2, d = −5
- T30 = 2 + 29 × −5 = −143
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.
Great work. Here's what to try next: