Sequences and series

Sequences and series

1. The 'n'th term of a sequence in sometimes called the general term

   • 'n'th term of a sequence is given by Un= 3n-1. Work out the, first, third and the nineteenth term
     • U1= 3*1-1= 2
     • U3= 3*3-1= 8
     • U19= 3*19-1= 56
   • Find the value of 'n' for which Un has the given value
     • Un= n^2- 7n +12, Un=72
       • 72= n^2-7n+12
         • 0=(n-12)(n+5)
           • n=12

2. a+ (n-1) d

   • For the arithmetic series 5+9+13+17+21+...+805. find the number of terms, which term of the series would be129?
     • 805= 5 +(n-1)*a
       • 805= 4n-1
         • n=201
           • There are 201 terms in this series
     • 129= 5+(n-1*4
       • 129=4n+1
         • 128=4n
           • n=32
             • The 32nd term is 129

3. S'n'= n/2 [2a+ (n-1)d]

4. S'n'= n/2 (a+L)