Question

Find the pattern and use it to list the nth term in the sequence.

Answer 1

`(1)/(n^5)`

1) Note that each term we have a number so let's write out a diagram to better get it:

`\begin{gathered} a_1----1 \\ a_2----(1)/(32) \\ a_3----(1)/(243) \\ a_4----(1)/(1024) \\ a_5----(1)/(3125) \end{gathered}`

On the left is the term, and on the right the given value:

2) Notice that we can rewrite that sequence in another way:

`\begin{gathered} a_1-------(1)/(1^5) \\ a_2-------(1)/(2^5) \\ a_3-------(1)/(3^5) \\ a_4-------(1)/(4^5) \\ a_5-------(1)/(5^5) \end{gathered}`

3) So as we can see the nth term can be written this way:

`a_n-----(1)/(n^5)`

And that's the answer