Math worksheet featuring ten problems on sequences, covering topics such as finite vs. infinite sequences, common differences, recursive and explicit formulas, and term calculations.

A worksheet with ten math problems involving sequences, including identifying finite or infinite sequences, finding common differences, writing recursive and explicit rules, and calculating specific terms.

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Show Answer Key & Explanations Step-by-step solution for: Arithmetic Sequences Notes and Worksheets - Lindsay Bowden

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1. The common difference is -6.
2. The first 5 terms are: 8, 2, -4, -10, -16.
3. The sequence is infinite.
4. The next 5 terms are: 40, 55, 70, 85, 100.
5. Recursive rule: a₁ = 6, aₙ = aₙ₋₁ + 19 for n ≥ 2.
6. Explicit rule: aₙ = 3 + (n-1)(-2) or aₙ = 5 - 2n.
7. Recursive rule: a₁ = 17, aₙ = 2aₙ₋₁ for n ≥ 2.
8. Explicit rule: aₙ = 3·(-2)ⁿ⁻¹; a₁₀ = 3·(-2)⁹ = -1536.
9. Explicit rule: aₙ = 9·(-2)ⁿ⁻¹; a₁₂ = 9·(-2)¹¹ = -18432.
10. Recursive rule: a₁ = 6, aₙ = aₙ₋₁ + 3 for n ≥ 2; a₁₅ = 48.

Parent Tip: Review the logic above to help your child master the concept of recursive and explicit formulas worksheet.

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