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!

1 Answer
Feb 25, 2018

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)