MAT 112 -03/04 In-class Homework

Section 10.1 #10, 26, 54.

10. Write the first five terms of the sequence beginning with n = 1.
    a_n = (3n² - n + 4) / (2n² + 1).
    a₁ = (3*1² - 1 + 4) / (2*1² + 1) = 2.
    a₂ = (3*2² - 2 + 4) / (2*2² + 1) = 14/9.
    a₃ = (3*3² - 3 + 4) / (2*3² + 1) = 28/9.
    a₄ = (3*4² - 4 + 4) / (2*4² + 1) = 16/11.
    a₅ = (3*5² - 5 + 4) / (2*5² + 1) = 74/51.

26. Write the first five terms of the sequence defined recursively.
    a₁ = 15, a_k+1 = a_k + 3.
    a₂ = 15 + 3 = 18.
    a₃ = 18 + 3 = 21.
    a₄ = 21 + 3 = 24.
    a₅ = 24 + 3 = 27.

54. Write an expression for the most apparent n^th term of the sequence, with n beginning with 1.
    1/3, 2/9, 4/27, 8/81.
    Clearly the denominator is in powers of 3: 3¹, 3², 3³,….
    The numerator is in powers of 2: 2⁰, 2¹, 2², ….
    We have a_n = 2^{n - 1} / 3ⁿ.

Essential Trigonometry, Math Links

by Jack Tompkins