Topic 2.3 – Linear Growth and Arithmetic Sequences

Linear Growth and Arithmetic Sequences discusses the recursion of repeated addition to arrive at an arithmetic sequence. The explicit formula is also discussed, including its connection to the recursive formula and to the Slope-Intercept Form of a Line. We prefer sequences to begin with the term [latex]a_0[/latex] rather than [latex]a_1[/latex] so that the connection between the starting point [latex]a_0[/latex] and the [latex]y[/latex]-intercept of a line can be established. Therefore, the explicit formula is given as [latex]a_n = a_0 + nd[/latex] rather than [latex]a_n = a_1 + (n-1)d[/latex].

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