Today's soundtrack is The Advantage: Elf Titled, a really cool instrumental Nintendocore album that features prog rock covers of classic NES-era video game tunes.
This evening, I'm working on arithmetic series, which are related to arithmetic sequences. An arithmetic sequence is a set of numbers with the same difference between each one (2, 4, 6, 8, 10; or 3, 7, 11, 15, 19); an arithmetic series adds the terms in an arithmetic sequence: 2+4+6+8+10, etc.
To write an expression for the nth term of an arithmetic sequence, we say Tn = [the number of the first term] plus [the common degrees between each term] times (n - 1). For example, Tn = 1+4 (n-1).
When we have an arithmetic sequence, we call each of its numbers "terms," and we name them by their position in the sequence: t1, t2, t3, etc. Similarly, series' are identified by their sums, the combined value of the terms up to that point. S1 = t1, S2 = t1+t2, S3 = t1+t2+t3, and so on. We call these sums "partial sums" (Pearson Pre-Calculus 11, p. 15).
I'll keep working on this tomorrow; I'm exhausted.