I just finished my twenty-third consecutive day of writing mathematics problems for a high-school mathematics textbook’s teacher’s resource appendix. I’m now working on a chapter about sequences and series. Today I completed one of the more challenging lessons that I’ve done so far, which involved sequences that are not arithmetic or geometric sequences. An example of an arithmetic sequence is 1, 3, 5, 7, 9, …, where 2 is being added to each successive term in the sequence. An example of a geometric sequence is 1, 2, 4, 8, 16, …, where 2 is being multiplied to each successive term in the sequence. But what about a sequence like 1, 5, 13, 29, 61, …? How do you define this sequence? That’s what I wrote about today.

Tags: Math, Mathematics