12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 12th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Sequences & Series12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 16th term of the arithmetic sequence 3, −2, −7, −12, …
Answer: −72
- a = 3, d = −5
- T16 = 3 + 15 × −5 = −72
2.For the arithmetic sequence 15, 12, 9, 6, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 18
- d = 12 − 15 = −3
- Tₙ = a + (n − 1)d = 15 + (n − 1) × −3 = −3n + 18
3.Find the 22th term of the arithmetic sequence 4, 7, 10, 13, …
Answer: 67
- a = 4, d = 3
- T22 = 4 + 21 × 3 = 67
4.Find the 13th term of the arithmetic sequence −2, −8, −14, −20, …
Answer: −74
- a = −2, d = −6
- T13 = −2 + 12 × −6 = −74
5.Find the 23th term of the arithmetic sequence −7, −8, −9, −10, …
Answer: −29
- a = −7, d = −1
- T23 = −7 + 22 × −1 = −29
6.For the arithmetic sequence 20, 24, 28, 32, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 16
- d = 24 − 20 = 4
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 4 = 4n + 16
7.For the arithmetic sequence 1, 7, 13, 19, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 5
- d = 7 − 1 = 6
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 6 = 6n − 5
8.For the arithmetic sequence −4, −5, −6, −7, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 3
- d = −5 − (−4) = −1
- Tₙ = a + (n − 1)d = −4 + (n − 1) × −1 = −n − 3
9.Find the 9th term of the arithmetic sequence 0, 8, 16, 24, …
Answer: 64
- a = 0, d = 8
- T9 = 0 + 8 × 8 = 64
10.For the arithmetic sequence 5, 8, 11, 14, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 2
- d = 8 − 5 = 3
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 3 = 3n + 2
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: