Recursively defined sequences
Types of exercises: terms of a recursively defined sequence, a recursive formula for the given terms, sum of the first terms of a recursively defined sequence.
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The sequence (aₙ) is defined recursively for n ≥ 1. Compute the given sum of its first terms
a₁ = −4, aₙ₊₁ = −aₙ + 1, a₁ + a₂ + a₃ + a₄ = ?
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the indicated term
a₁ = 7, aₙ₊₁ = −2aₙ − 5, a₄ = ?
The sequence (aₙ) is defined recursively for n ≥ 1 and its first terms are given below. Which formula describes this sequence?
2, 3, 4, 5, …
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the given sum of its first terms
a₁ = −1, aₙ₊₁ = −3aₙ − 5, a₁ + a₂ + a₃ + a₄ = ?
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the indicated term
a₁ = 2, aₙ₊₁ = aₙ − 2n, a₃ = ?
The sequence (aₙ) is defined recursively for n ≥ 1 and its first terms are given below. Which formula describes this sequence?
0, −3, −12, −39, …
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the given sum of its first terms
a₁ = 2, aₙ₊₁ = aₙ + 4, a₁ + a₂ + a₃ + a₄ + a₅ = ?
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the indicated term
a₁ = 2, aₙ₊₁ = −aₙ + 2, a₄ = ?
The sequence (aₙ) is defined recursively for n ≥ 1 and its first terms are given below. Which formula describes this sequence?
−4, −1, −4, −1, …
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the given sum of its first terms
a₁ = −7, aₙ₊₁ = aₙ + n − 3, a₁ + a₂ + a₃ + a₄ + a₅ = ?
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