Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Sequences & SeriesYear 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 6 terms of the geometric sequence 7, 28, 112, 448, …
Answer: 9555
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × (46 − 1) ÷ (4 − 1)
- = 9555
2.Find the 6th term of the geometric sequence −2, −4, −8, −16, …
Answer: −64
- a = −2, r = 2
- T6 = −2 × 25 = −64
3.For the geometric sequence −2, −4, −8, −16, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −2 × 2n − 1
- r = −4 ÷ (−2) = 2
4.For the arithmetic sequence 20, 18, 16, 14, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 22
- d = 18 − 20 = −2
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −2 = −2n + 22
5.For the arithmetic sequence 20, 21, 22, 23, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 19
- d = 21 − 20 = 1
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 1 = n + 19
6.For the geometric sequence 1, 5, 25, 125, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 1 × 5n − 1
- r = 5 ÷ 1 = 5
7.Find the 5th term of the geometric sequence 7, 35, 175, 875, …
Answer: 4375
- a = 7, r = 5
- T5 = 7 × 54 = 4375
8.Find the 5th term of the geometric sequence 4, 8, 16, 32, …
Answer: 64
- a = 4, r = 2
- T5 = 4 × 24 = 64
9.Find the 16th term of the arithmetic sequence −1, −5, −9, −13, …
Answer: −61
- a = −1, d = −4
- T16 = −1 + 15 × −4 = −61
10.For the arithmetic sequence −10, −16, −22, −28, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n − 4
- d = −16 − (−10) = −6
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −6 = −6n − 4
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