Q: Should I be closing apps after use?

A lot of apps don't remain active after you go back to the home screen or switch into a different app, so for most it's not necessary to close them - but it doesn't do any harm to occasionally go into the taskbar and close them all.

I make it a point to shut down all apps at the end of the day.

Not closing the apps doesn't affect the speed etc, but it drains battery faster as these apps are still running in the background. So it's a preference unless you need to save battery hope this helps!

Understanding multitasking

http://support.apple.com/kb/HT4211

All apps are running in the background every time you return to the home screen unless you delete them from the multitasking bar at the bottom. they aren't necessarily 'active', but they still use up power since they still run in the background. the bar at the bottom is actually so that people can switch between open apps easily, which means they are actually all running.

Most don't, they just become 'recently used'. I tend to just leave the apps that I frequently use on the taskbar and close all others, so I usually only have 4 or 5 on there - so depending upon what I've been doing on the iPad, I might close apps a couple of times a day.

Most are not running or using any resources, they are just 'recently used' (an app has to be coded to make use of multitasking) - see the page that Diavonex has linked to.

You are most welcome