Question

How to find the nth term of a sequence?

I understand the basics,
e.g
the expression for 4,9,14,19... would be `5n-1` .

But the question below has me stuck.

Find an expression for the nth term for the sequence below:

`1/2, 2/3, 3/4,4/5...`

Thanks!

Answer 1

`a_n=(n)/(n+1)`

Explanation:

We have the first one one over two, second one two over three, and so on.

For the numerators, they start with one and gets larger by 1.
`a_n=n`

For the denominators, they start with two and gets larger by 1.

`a_n=n+1`

We divide the numerator by the denominator to get `a_n=(n)/(n+1)`