arithmetic sequence

arithmetic sequence

1. to be arithmetic a sequence must have a common difference

   • recursive formula
     • what is it ?
       • a function rule that relates each term to ones before it
     • how to write one?
       • 1.find the common difference
       • 2.a(n) or called the term we want
       • 3. a(n-1) or the previous term
       • common difference
     • to find a term you must
       • plug the term in function?
         • a(n)=a(n-1)+D in "a(n-1)" plug in first term
   • explicit formula
     • what is it?
       • a much more efficient way to find a term in a sequence
     • how to write one?
       • 1. find common fifference
       • 2.a(n)= or term we want
       • 3. a(1)+ or called 1st term
       • 4.(n-1) or term we want minus 1t
       • 5. (d) times the common difference
     • to find a term you
       • plug the term into the function?
         • a(n)=a(1)+(n-1)(d)
   • now try
     • 10,20,30,40... given this sequence is this arithmetic?
       • yes it is common difference of 10
       • write a recursive formula
         • a(n)= A(n-1) + or - d a(n)=a(n-1)+10   A(1)=10
         • find the 5 term
           • a(5)=40+10 a(5)=50
       • write a explicit formula
         • a(n)= a(1)+ (n-1) (d) A(n)= 10+ (n-1) (10)
         • find the 5 term
           • a(5)=10 + 9(14) a(5)= 136