10th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the sum of the first 10 terms of the arithmetic sequence 5, 9, 13, 17, …
Answer: 230
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × 5 + 9 × 4)
- = 230
2.For the arithmetic sequence 20, 25, 30, 35, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 15
- d = 25 − 20 = 5
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 5 = 5n + 15
3.For the arithmetic sequence 6, 11, 16, 21, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 1
- d = 11 − 6 = 5
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 5 = 5n + 1
4.Find the 24th term of the arithmetic sequence 16, 25, 34, 43, …
Answer: 223
- a = 16, d = 9
- T24 = 16 + 23 × 9 = 223
5.For the arithmetic sequence 0, −5, −10, −15, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 5
- d = −5 − 0 = −5
- Tₙ = a + (n − 1)d = 0 + (n − 1) × −5 = −5n + 5
6.For the arithmetic sequence 16, 12, 8, 4, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 20
- d = 12 − 16 = −4
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −4 = −4n + 20
7.Find the sum of the first 6 terms of the geometric sequence 5, 15, 45, 135, …
Answer: 1820
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (36 − 1) ÷ (3 − 1)
- = 1820
8.For the geometric sequence 5, 20, 80, 320, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 5 × 4n − 1
- r = 20 ÷ 5 = 4
9.Find the sum of the first 9 terms of the geometric sequence 8, 40, 200, 1000, …
Answer: 3906248
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (59 − 1) ÷ (5 − 1)
- = 3906248
10.Find the sum of the first 23 terms of the arithmetic sequence −5, −7, −9, −11, …
Answer: −621
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × −5 + 22 × −2)
- = −621
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.