How do you find the nth term rule for #1/2,1,3/2,2,...#?
firstly see what the terms increase by
so nth term is of the form
use the first term and
a quick mental check on the next few terms confirms the result.
The sequence might be easier to recognise as an AP if the terms are written as improper fractions:
An even better way to write this is in halves:
It is then immediately obvious that each term is just
Using the formula/ general rule:
The nth term is written as
All the values you need are available from the sequence.