Recursive Formulas Worksheet
Explore sequences defined by recursive formulas with this Grade 8 math worksheet, including finding terms and writing formulas.
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Recursive Formulas
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Read each question carefully and follow the instructions to determine terms in sequences or write recursive formulas.
1. Find the first five terms of the sequence defined by a₁ = 3 and aₙ = aₙ₋₁ + 4 for n > 1.
2. Find the first four terms of the sequence defined by a₁ = 10 and aₙ = 2 * aₙ₋₁ - 5 for n > 1.
3. A sequence starts with 5, 10, 15, 20, ... The recursive formula is a₁ = and aₙ = .
4. A sequence starts with 2, 6, 18, 54, ... The recursive formula is a₁ = and aₙ = .
5. Which recursive formula describes the sequence: 7, 10, 13, 16, ...?
a₁ = 7, aₙ = aₙ₋₁ + 3
a₁ = 7, aₙ = 3aₙ₋₁
a₁ = 7, aₙ = aₙ₋₁ - 3
a₁ = 7, aₙ = aₙ₋₁ + 7
6. Given the recursive formula a₁ = 20 and aₙ = aₙ₋₁ / 2, what is the third term (a₃) of the sequence?
5
10
20
40
7. A plant grows 2 cm each week. If it starts at 5 cm tall, write a recursive formula for its height after 'n' weeks.