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Abstract

An ordered set of numbers forms a sequence, the order being determined by an algebraic formula. For example
  1. (a)
    2, 5, 8, 11 is a sequence which could be formed from
    $$ {T_n} = 2 + 3\left( {n - 1} \right) = 3n - 1 $$
    T n is the nth term. (This is an arithmetric progression.)
     
  2. (b)

    2, 8, 11, 5 could be formed from \( {T_n} = 3{n^3} - \frac{{45}}{2}{n^2} + \frac{{105}}{2}n - 31 \).

     
  3. (c)

    2, 10, 50, 250 could be formed from T n = 2 × 5n−1 (a geometric progression—G.P.).

     
  4. (d)

    2, 1, ½, ¼ could be formed from T n = 2 × (½)n−1 = (½)n−2 (another geometric progression).

     
  5. (e)
    $$\frac{1} {{1.3}},\frac{1} {{3.5}},\frac{1} {{5.7}},\frac{1} {{7.9}}\;is\;such\;that\;{T_n} = \frac{1} {{(2n - 1)(2n + 1)}}$$
     
  6. (f)
    $$1,\frac{1} {{2!}},\frac{1} {{3!}},\frac{1} {{4!}}\;is\;such\;that\;{T_n} = \frac{1} {{n!}}$$
     

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Copyright information

© H. J. Halstead and D. A. Harris 1963

Authors and Affiliations

  1. 1.Mathematics DepartmentRoyal Melbourne Institute of TechnologyAustralia

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