Answer:
Explicit
Step-by-step explanation:
Given
[tex]Term: a_{50[/tex]
Required
Explicit or Recursive; which is easier
The explicit form is easier.
Take for instance, the explicit form of the sequence is:
[tex]a_n = 2n + 1[/tex]
And the recursive form is:
[tex]a_n = a_{n-1} + 2[/tex]
To find [tex]a_{50}[/tex] in [tex]a_n = 2n + 1[/tex]
You simply substitute 50 for n and then solve for [tex]a_n[/tex]
Which gives:
[tex]a_{50} = 2*50 + 1 = 101[/tex]
The case is different in: [tex]a_n = a_{n-1} + 2[/tex]
First, you substitute 50 for n
[tex]a_{50} = a_{50-1} + 2[/tex]
[tex]a_{50} = a_{49} + 2[/tex]
Next, you need to calculate a49.
This action continues until you get to a1
Then you evaluate the corresponding expressions from a1 to a49 before you get a50.
Hence, the explicit form is easier.
