Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 14th term of the arithmetic sequence −5, 2, 9, 16, …
Answer: 86
- a = −5, d = 7
- T14 = −5 + 13 × 7 = 86
2.Find the 7th term of the geometric sequence 5, 20, 80, 320, …
Answer: 20480
- a = 5, r = 4
- T7 = 5 × 46 = 20480
3.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
4.Find the 15th term of the arithmetic sequence 16, 11, 6, 1, …
Answer: −54
- a = 16, d = −5
- T15 = 16 + 14 × −5 = −54
5.Find the sum of the first 7 terms of the geometric sequence 1, 5, 25, 125, …
Answer: 19531
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (57 − 1) ÷ (5 − 1)
- = 19531
6.Find the sum of the first 11 terms of the arithmetic sequence 3, 0, −3, −6, …
Answer: −132
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × 3 + 10 × −3)
- = −132
7.Find the 6th term of the geometric sequence 5, 10, 20, 40, …
Answer: 160
- a = 5, r = 2
- T6 = 5 × 25 = 160
8.Find the sum of the first 19 terms of the arithmetic sequence −2, 5, 12, 19, …
Answer: 1159
- Sₙ = n/2 × (2a + (n − 1)d)
- = 19/2 × (2 × −2 + 18 × 7)
- = 1159
9.Find the 5th term of the geometric sequence 3, −6, 12, −24, …
Answer: 48
- a = 3, r = −2
- T5 = 3 × (−2)4 = 48
10.Find the 16th term of the arithmetic sequence −1, 6, 13, 20, …
Answer: 104
- a = −1, d = 7
- T16 = −1 + 15 × 7 = 104
Marking tips
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