11th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 9th term of the arithmetic sequence 6, 5, 4, 3, …
Answer: −2
- a = 6, d = −1
- T9 = 6 + 8 × −1 = −2
2.Find the 27th term of the arithmetic sequence −10, −2, 6, 14, …
Answer: 198
- a = −10, d = 8
- T27 = −10 + 26 × 8 = 198
3.For the arithmetic sequence 20, 29, 38, 47, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 11
- d = 29 − 20 = 9
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 9 = 9n + 11
4.For the arithmetic sequence 3, −3, −9, −15, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 9
- d = −3 − 3 = −6
- Tₙ = a + (n − 1)d = 3 + (n − 1) × −6 = −6n + 9
5.For the arithmetic sequence −1, 3, 7, 11, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 5
- d = 3 − (−1) = 4
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 4 = 4n − 5
6.For the arithmetic sequence 5, 0, −5, −10, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 10
- d = 0 − 5 = −5
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −5 = −5n + 10
7.For the arithmetic sequence 7, 9, 11, 13, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 5
- d = 9 − 7 = 2
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 2 = 2n + 5
8.Find the 26th term of the arithmetic sequence 8, 5, 2, −1, …
Answer: −67
- a = 8, d = −3
- T26 = 8 + 25 × −3 = −67
9.Find the 13th term of the arithmetic sequence 11, 10, 9, 8, …
Answer: −1
- a = 11, d = −1
- T13 = 11 + 12 × −1 = −1
10.For the arithmetic sequence 7, 10, 13, 16, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 4
- d = 10 − 7 = 3
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 3 = 3n + 4
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: