How can I find the general formula to this arithmetic sequence? $$\frac{-1}{4}, \frac{-1}{8}, \frac{-1}{12}, \frac{-1}{16}, \frac{-1}{20}, \frac{-1}{24}$$
I have noticed that firstly, they increase by four, and they are all multiples of four. I have some guesses on the general formula, but I am not sure.
The numerators remain $-1$ throughout, the denominators go: $4,8,12,16,20,24...$, which are all multiples of $4$. In terms of spotting this, be sure to learn times tables to make it easier. Since they are all multiples of $4$, a general term is $4n$. Hence the general formula is $\frac{-1}{4n}$