February 4th 2018 archive

04
Feb
2018

Week 1 – My Arithmetic Sequence

categories: Math 11

 

4, 9, 14, 19, 24

d=5, t_1=4

 

t_n=t_1+(n-1)d

 

t_n=4+(n-1)5

 

t_n=4+5n-5

 

t_n=5n-1

using this information, we can find any value of t using the equation t_n=5n-1. We can plug in any term into n to find t_n

 

this equation will work for any term within the sequence, as long as the starting term and common difference are constant. If either of these change it is no longer an arithmetic sequence.

To find S_{50}, the sum of all 50 terms, we must use the equation S_n={n}{2}(a+1)

In this equation, n= number of terms(50) and a= the first term(4)

 

S_{50}={50}{2}(4+1)

 

S_{50}=25(5)

 

S_{50}=125