The topic I am choosing to write about this week in math is something called “Arithmetic Series”. A short explanation of what arithmetic series are, is basically when you have a regular sequence but need to add all the number in the sequence together to find the sum (Ex. Sn =)

So, if your sequence was 1,2,3…98,99,100 – you would know that there’re a total of 100 terms in the sequence. After that you would take the amount of all the terms (100) divide that by 2, then take the first and last term ( / ) add those together and multiply it by the result of the division.

Ex. Sn= n/2 ( + )

Sn = 100/2 (1 + 100)

Sn = 50(101)

Sn = 5050

Example:

       

The question I am choosing to explain is one from this week’s assignment. The question gives you two terms ( = 1.5 / = 58.5), then asks you to find .

Step 1 – find the difference

I did this by doing the basic arithmetic sequence formula [ = + (n -1) (d) ]

Step 2 – Find the 15^th term

Once again, I did the basic arithmetic sequence formula

Step 3 – Find Sum of numbers

For this step I did the formula we were taught to find Sn [ Sn = n/2 ( + )

This question took some time to do, as I was slowly figuring out each step one by one by myself. I am very glad that I finally figured it out and came to this conclusion.