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The arithmetico-geometric sequence: an application of linear algebra. (English) Zbl 1343.97006

Summary: In this paper, we present a linear algebra-based derivation of the analytic formula for the sum of the first \(n\)th terms of the arithmetico-geometric sequence. Furthermore, the advantage of the derivation is briefly discussed.

MSC:

97H60 Linear algebra (educational aspects)
97I30 Sequences and series (educational aspects)
15A18 Eigenvalues, singular values, and eigenvectors
40A05 Convergence and divergence of series and sequences
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References:

[1] DOI: 10.1142/5909 · doi:10.1142/5909
[2] Parmenter MM. Theory of interest and life contingencies with pension applications: a problem solving approach. 3rd ed. Winsted (CT): ACTEX Publications; 1999. p. 58–59.
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