For our first week of precalc 11, one of the things we learned were arithmetic series. An arithmetic series is the sum of the terms in an arithmetic sequence. An arithmetic sequence means that the difference between consecutive terms must be constant. That constant value is called the common difference.

What I struggled with more was arithmetic series. Figuring out which numbers to plug into the formula became confusing for me.

Ex from #6, pg19 : For each arithmetic series, determine the indicated value

a) – 4 – 11 – 18 – 25 – … ; determine S28

When I first started solving this question, I thought to myself about the formula we used for arithmetic sequences : tn = t1 + (n – 1)(d)

I learned here that in this equation I had to figure out S28 by using t28 as tn 

By figuring that out, I was able to do this :

 

After being able to find t28 , I was able to now use the arithmetic series formula to figure out the S28 : Sn = n/2 (t1 + tn)

 

The main I learned in this question that to find the sum of the 28 terms, I first had to figure out what 28 terms equaled to. I also got more familiar with the vocabulary such as…

Sum of the numbers : Sn 

First term : t1

Last term : t28

Arithmetic series : sum of the terms in an arithmetic sequence

Arithmetic sequences : in a sequence, the difference between consecutive terms must be constant