Our week 1 blog post is about arithmetic sequences, and how to display their rule, sum, or specific sequence number. In this short post, I will show each step to solving an arithmetic sequence in all of the above ways.

My sequence of 5 numbers consists of:

5,12,19,26,33

Formula: t_n=t_1+(n-1)d

Rule: t_n=5+(50-1)7

Find: t_{50}:

t_n=5+(n-1)7

 

t_{50}=5+(50-1)7

 

t_{50}=5+(49)7

 

t_{50}=5+343

 

t_{50}=<em>348</em>

 

Now the next step is to add the first 50 terms in this sequence, or S_{50}:

Formula: S_n=\frac{n}{2}(t_1+t_n)

Find: S_{50}:

S_{50}=\frac{50}{2}(5+348)

 

S_{50}=\frac{50}{2}(353)

 

S_{50}=25(353)

 

S_{50}=8825