Question

In comparing the two written forms of a sequence, which is easier to find a50, the explicit form or the recursive form?

Answer 1

Explicit

Explanation:

Given

`Term: a_{50`

Required

Explicit or Recursive; which is easier

The explicit form is easier.

Take for instance, the explicit form of the sequence is:

`a_n = 2n + 1`

And the recursive form is:

`a_n = a_(n-1) + 2`

To find
`a_(50)` in
`a_n = 2n + 1`

You simply substitute 50 for n and then solve for
`a_n`

Which gives:

`a_(50) = 2*50 + 1 = 101`

The case is different in:
`a_n = a_(n-1) + 2`

First, you substitute 50 for n

`a_(50) = a_(50-1) + 2`

`a_(50) = a_(49) + 2`

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.