Question

How can you represent the terms of a sequence explicitly? How can you represent them recursively?

Provide mathematical examples to support your opinions.

Answer 1

a sequence can be written by a summation

Answer 2

Explicitly means you define it as a function of \(n\). \[
a_n = f(n)
\]E.G.\[
a_n = 54 - 5n
\]
Recursively means you define it in terms of other parts of the sequence
E.G. \[
a_n = a_{n-1} + a_{n+1} \cdot a_{n/2}
\]

Answer 3

or simply calculated in other words you can have

1+2+3+4
or

\[\sum_{n=0}^\infty n+1\]