The n-th number in a given sequence of numbers might have more than one commonly‑encountered form. In the case of a sequence of equally‑spaced numbers, there are the following two forms that are commonly encountered: first form: a + (n – 1)d second form: (a – d) + nd They are algebraically equivalent, of course. … Continue reading forms of the n-th number in a sequence →

Sums are usually of arbitrary numbers, but sometimes a sum has a theme. A good example of this concerns the odd numbers, namely, the sum of the first n odd numbers. This thematic summation is of interest because of its gem of an answer: ‘n squared’. For example, the first 3 odd numbers are 1, … Continue reading thematic summation →

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