Weekly Reflection 11-23-18

Recursive and Explicit forms:
There is no objective


Recursive Example: 
Find the fifth term of a recursive define sequence a(1)=1 a(n)=a(n-1)+2n+1 where n is greater than or equal to two.
a(1)=1
a(2)=a(2-1)+2(2)+1=a(1)+4+1=1+5=6
a(3)=a(3-1)+2(3)+1=6/a(2)+6+1=13
a(4)=a(4-1)+2(4)+1=13/a(3)+8+1=22
a(5)=a(5-1)+2(5)+1=22/a(4)+10+1=33
33 is the fifth term


Explicit Example:
Find the first four terms of the sequence given by a(n)=2n(-1)^n

        ______            _______            _______           _______       
          a1                     a2                       a3                     a4

a1=2(1)(-1)^1= -2                             a2=2(2)(-1)^2= 4

a3=2(3)(-1)^3= -6                             a4=2(4)(-1)^4= 8
-2,4,-6,8 are the first four terms



One misconception I had was with the recursive form, I was unsure on how to continue adding on after I had my first answer but I resolved my problem after I asked for help from a friend.

EQ: How do you determine whether a sequence converges or diverges?
The sequence converges when the common ratio is less than 1 and the sequence diverges when the common ratio is greater than 1.



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