My iMac has become so slow can I upgrade memory

What is your memory and storage?

On no evidence other than slowness, you probably have the 8 GB hard disk drive iMac configuration, and that configuration will be slow.

Here is why: Why is my hard disk drive iMac so slow? - Apple Community

That article also links to a workaround: Use an external SSD as your startup disk … - Apple Community

Adding memory in the iMac 27” is feasible, but it’s usually the hard disk that’s causing the slow. More memory helps, an SSD helps more. Adding memory in many of the iMac 21.5” variants is a project. An Apple reseller might be willing to undertake that internal memory upgrade on the iMac 21.5”, and swapping in an SSD, but that’s not going to be cheap.

It’s also possible you have a different configuration or different issue too (again, above is a guess), such as a failing Mac.

Always have complete and current backups, if you don’t already have those.

Upgrading RAM is not going to increase your speed unless you have a specific app with specific RAM needs.

The best way to speed things up is to stop all apps loading in background, be sure 15-20% of your disk is COMPLETELY unused and by going to an SSD as a boot drive. Even an external SSD is faster than an internal HDD ...and you didn't say.

Not necessarily. For less than $100US four years ago, I went with an external SSD on my 2015 21.5" iMac. Disk speed improvement was 5 fold ... 90MBps to 450 MBps. It now is joy to use.

It just takes little work.