If you are "jailbroken" there are many tweaks that allow different ways to view paused apps.
i Use Multifl0w
For completet control over iOS multitasking i use these:
Multifl0w
MultiCleaner
Backgrounder
Mutifl0w just gives you 2 different ways to "view" paused apps, and MultiCleaner and Backgrounder improve the multitasking functionality. I truly cannot live without MultiCleaner. Using Activator you can assign any gesture/action for "quit current app", "quit all apps at once", and minimize app. With the combination of Activator and MultiCleaner i can simply swipe up from the bottom right-side of my screen to bring up the app switcher, then just drag any app up and out of the switcher. I love that.lol. No double pressing the home button, no tapping and holding on an icon til it wiggles to quit it. Just swipe up, and swipe up and out any app in the switcher.
Other tweaks that offer different ways to "view" paused apps are:
Imperium (not bad actually.If you can get use the UI. I dont really like the UI, but the functionality the UI offers is impressive, and has really improved since it's first initial version)
CardSwitcher (same thing as Multifl0w but a little better IMO. just have to respring every time you make a change, but only have to apply changes to the settings once)
Zephyr (control and view app switcher and paused apps with "swipe" gestures. Very nice tweak, and I would use it the "swipe up to activate switcher" did not conflict with Activators "swipe up from screen bottom" actions. So I just use Activator to pull up the app switcher with a quick swipe up from the bottom of the screen)
Aero (View paused apps via the app icon in a flow effect over the springboard (or blank background))
The only way to really see what these tweaks do is to YouTube them or something.
If you are not jailbroken, nor plan on jailbreaking........................Well....................Sorry for wasting your time
On a side note:
Most apps have pretty much no effect at all if they are paused, while certain apps do. like GPS apps, and anything that streams media.
But for the most part 99% of all apps cannot run in the background. They are paused in RAM and iOS frees that RAM when the phone needs it.
Closing an app that streams data, like Pandora, or a lot of navigation apps will have a small effect when free'd, but only those large apps that actually use Apple'e API for multitasking will make a "small" difference.
Other apps that dont do anything but remain in a "paused" state don't make much of a difference when closed. But nevertheless, is not ever a bad idea to free your RAM from time to time. Otherwise it is pretty pointless to constantly close the apps in your switcher. But hey, helps with the OCD.lol