Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 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 16 terms of the arithmetic sequence 11, 17, 23, 29, …
Answer: 896
- Sₙ = n/2 × (2a + (n − 1)d)
- = 16/2 × (2 × 11 + 15 × 6)
- = 896
2.Find the 15th term of the arithmetic sequence 8, 3, −2, −7, …
Answer: −62
- a = 8, d = −5
- T15 = 8 + 14 × −5 = −62
3.Find the 5th term of the geometric sequence −3, −9, −27, −81, …
Answer: −243
- a = −3, r = 3
- T5 = −3 × 34 = −243
4.Find the 21th term of the arithmetic sequence 3, 4, 5, 6, …
Answer: 23
- a = 3, d = 1
- T21 = 3 + 20 × 1 = 23
5.Find the 7th term of the geometric sequence −3, −12, −48, −192, …
Answer: −12288
- a = −3, r = 4
- T7 = −3 × 46 = −12288
6.Find the sum of the first 7 terms of the geometric sequence −1, 2, −4, 8, …
Answer: −43
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × ((−2)7 − 1) ÷ (−2 − 1)
- = −43
7.Find the sum of the first 26 terms of the arithmetic sequence 14, 23, 32, 41, …
Answer: 3289
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 14 + 25 × 9)
- = 3289
8.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
9.Find the 12th term of the arithmetic sequence 13, 21, 29, 37, …
Answer: 101
- a = 13, d = 8
- T12 = 13 + 11 × 8 = 101
10.For the geometric sequence 2, 10, 50, 250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 2 × 5n − 1
- r = 10 ÷ 2 = 5
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