Sequences (Calculus)

(Finney, AP Calculus BC)

Find the first 3 terms and the 8th term of the sequence:
a₁ = 4 aₙ = aₙ₋₁ − 2, n ≥ 2
u₁ = −5, u₂ = 2, uₙ = uₙ₋₁ + uₙ₋₂, n ≥ 3.Find the first 3 terms and the 8th term.
Given 10, 27, 44, 61, … Find a recursive rule and an explicit rule for the nth term.
Given 1.5, 2.25, 3.375 … Find a recursive and explicit rule for the sequence.
Let {aₙ} be an arithmetic sequence where a₅ = 5 and a₉ = −3. Find an explicit rule for aₙ.
Given {uₙ} is a geometric sequence with a₆ = 3010 and a₉ = 3,010,000. Find an explicit rule.
Find the limit of aₙ = (2n + 1)/n
Find the limit of aₙ = (−1)ⁿ (n + 1)/(n² + 2)
Find the limit of aₙ = cos(nπ/2)
Use the Absolute Value Theorem to answer #8.

Find the first 3 terms and the 8th term of the sequence: a(1) = 4, a(n) = a(n-1) – 2, n >= 2
u(1) = -5, u(2) = 2, u(n) = u(n-1) + u(n-2), n >= 3. Find the first 3 terms and the 8th term.
Given 10, 27, 44, 61, … Find a recursive rule and an explicit rule for the nth term.
Given 1.5, 2.25, 3.375, … Find a recursive and explicit rule for the sequence.
Let {a(n)} be an arithmetic sequence where a(5) = 5 and a(9) = -3. Find an explicit rule for a(n).
Given {u(n)} is a geometric sequence with a(6) = 3010 and a(9) = 3,010,000. Find an explicit rule.
Find the limit of a(n) = (2n + 1)/n
Find the limit of a(n) = (-1)^n * (n + 1)/(n^2 + 2)
Find the limit of a(n) = cos(n*pi/2)
Use the Absolute Value Theorem to answer #8.