Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 8 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −292968
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (58 − 1) ÷ (5 − 1)
- = −292968
2.For the arithmetic sequence 9, 14, 19, 24, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 4
- d = 14 − 9 = 5
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 5 = 5n + 4
3.Find the 9th term of the geometric sequence −3, 6, −12, 24, …
Answer: −768
- a = −3, r = −2
- T9 = −3 × (−2)8 = −768
4.For the arithmetic sequence 3, 5, 7, 9, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 1
- d = 5 − 3 = 2
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 2 = 2n + 1
5.Find the sum of the first 13 terms of the arithmetic sequence 4, 7, 10, 13, …
Answer: 286
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 4 + 12 × 3)
- = 286
6.Find the sum of the first 26 terms of the arithmetic sequence 11, 18, 25, 32, …
Answer: 2561
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 11 + 25 × 7)
- = 2561
7.Find the sum of the first 19 terms of the arithmetic sequence −9, −12, −15, −18, …
Answer: −684
- Sₙ = n/2 × (2a + (n − 1)d)
- = 19/2 × (2 × −9 + 18 × −3)
- = −684
8.Find the sum of the first 27 terms of the arithmetic sequence 9, 10, 11, 12, …
Answer: 594
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × 9 + 26 × 1)
- = 594
9.Find the 18th term of the arithmetic sequence 17, 24, 31, 38, …
Answer: 136
- a = 17, d = 7
- T18 = 17 + 17 × 7 = 136
10.Find the 7th term of the geometric sequence −5, −25, −125, −625, …
Answer: −78125
- a = −5, r = 5
- T7 = −5 × 56 = −78125
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