# 09.29.2018: One Lesson of Math - Arithmetic Series (2/2) Today's soundtrack is Myles Kennedy: Year of the Tiger, a solo album by the singer of Alter Bridge, the band that Mark Tremonti is a guitarist in. It's interesting that Alter Bridge is the middle ground of these two artists' solo efforts: Mark Tremonti's solo albums are very heavy, almost metal; Kennedy's "Year of the Tiger" is more like a relaxed, bluesy country rock: no distortion guitars to be found here; lots of acoustic fingerpicking and crooning. It's an unexpectedly pleasant album.

This afternoon, I'm going to continue learning about arithmetic series. To recap where I left off last time: 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).

To find n when we know t1 and d, we solve for n in the following equation: tn = t1 + d (n - 1)

To find Sn when we know t1 and tn, we solve for Sn in the following equation: Sn = (n [t1 + tn] ) / 2.

To find Sn when we know t1 and d, we solve for Sn in the following equation: Sn = n/2 (2t1 + d [n-1] ).

To find t1 when we know Sn and tn, we solve for t1 in the following equation: Sn = n/2 (t1 + tn). To find d when we know t1 and Sn, we solve for d in the following equation: Sn = n/2 (2t1 + d [n-1] ).

To find n when we know t1 and S, we solve for n in the following equation: Sn = (n [t1 + tn] ) /2.

Using BEDMAS is really important in these equations