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A Study on Derivation of Identities for the Generalized Pell Sequence by Analogical Reasoning
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Analogical reasoning has been utilized in the extension of mathematical thinking and problem solving. In this study, by using conceptual analogy, we conjectured identities in the generalized Pell sequence corresponding to those in Heo([9])’s generalized Fibonacci sequence, and by using methodological analogy, we proved that the conjectured identities hold. Furthermore, we conjectured identities in certain forms of second-order linear recurrence sequences and proved their validity. This study expands identities from generalized Fibonacci sequences to those of certain second-order linear recurrence sequences by employing conceptual and methodological analogy.
Abstract
Analogical reasoning has been utilized in the extension of mathematical thinking and problem solving. In this study, by using conceptual analogy, we conjectured identities in the generalized Pell sequence corresponding to those in Heo([9])’s generalized Fibonacci sequence, and by using methodological analogy, we proved that the conjectured identities hold. Furthermore, we conjectured identities in certain forms of second-order linear recurrence sequences and proved their validity. This study expands identities from generalized Fibonacci sequences to those of certain second-order linear recurrence sequences by employing conceptual and methodological analogy.