Maths-Algebra: Sequences (nth Term)

Maths-Algebra: Sequences (nth Term)

1. Finding the nth Term

   • nth: 1 2 3 4
   • term: 5 8 11 14
   • Formula:
     • nth term = dn + (a - d)
       • d is the common difference and a is the first term
   • --> +3 -->
     • The difference between the numers is 3, so 3n is the formula.
       • 3n: 3 6 9 12
         • +2
           • You have +2 to get to the term
         • Term: 5 8 11 14
       • So the expression for the nth term is 3n + 2

2. Deciding if a Term is in a Sequence

   • It's dead easy!
     • Example:
       • The nth term of a sequence is given by n^2 - 2.
         • Find the 6th term in the sequence.
           • put n=6 into the expression:
             • 6^2 - 2 = 36 - 2
               • = 34
         • Is 45 a term in the sequence?
           • Set it equal to 45... n^2 - 2 = 45
             • n^2 = 47
               • n = √47 = 6.8556...
                 • n is not a whole number, so 47 is not in the sequence: n^2 - 2