Unlike computers, when you close an app on an iPhone, it immediately shuts down or gets suspended. You can resume from where you left off if an app is suspended, but it will not drain your battery while in the suspended mode as the OS automatically manages the processor and RAM of your device.

In some cases, the apps which are downloading content will still run in the background for 10 minutes before being suspended. Other apps can also run in the background forever if required. For example, audio apps will continue playing in the background and these apps should automatically suspend themselves when not in use.

So don't worry about manually closing the apps in your multitasking bar, as it won't drain your battery or cause your phone to slow down.