12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 30th term of the arithmetic sequence −7, −5, −3, −1, …
Answer: 51
- a = −7, d = 2
- T30 = −7 + 29 × 2 = 51
2.Find the 22th term of the arithmetic sequence 16, 10, 4, −2, …
Answer: −110
- a = 16, d = −6
- T22 = 16 + 21 × −6 = −110
3.Find the 12th term of the arithmetic sequence −9, 0, 9, 18, …
Answer: 90
- a = −9, d = 9
- T12 = −9 + 11 × 9 = 90
4.Find the 28th term of the arithmetic sequence 0, −6, −12, −18, …
Answer: −162
- a = 0, d = −6
- T28 = 0 + 27 × −6 = −162
5.For the arithmetic sequence 3, 10, 17, 24, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 4
- d = 10 − 3 = 7
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 7 = 7n − 4
6.Find the 26th term of the arithmetic sequence −8, −4, 0, 4, …
Answer: 92
- a = −8, d = 4
- T26 = −8 + 25 × 4 = 92
7.For the arithmetic sequence −2, 7, 16, 25, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 11
- d = 7 − (−2) = 9
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 9 = 9n − 11
8.For the arithmetic sequence 2, 3, 4, 5, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 1
- d = 3 − 2 = 1
- Tₙ = a + (n − 1)d = 2 + (n − 1) × 1 = n + 1
9.For the arithmetic sequence −3, −1, 1, 3, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 5
- d = −1 − (−3) = 2
- Tₙ = a + (n − 1)d = −3 + (n − 1) × 2 = 2n − 5
10.For the arithmetic sequence −10, −3, 4, 11, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 17
- d = −3 − (−10) = 7
- Tₙ = a + (n − 1)d = −10 + (n − 1) × 7 = 7n − 17
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: