I’ve researched the concept of force closing apps to save battery lifeon your mobile devices. Everything I’ve read indicates we should not do this and I’ve concluded the only reason to force close an app is if it freezes and becomes unresponsive. Here’s why.
It takes very little battery power to keep app data in memory. When you force close an app, you remove all that data from memory. When you reopen the app, your battery takes a hit because it requires more power to reload the app and its data than to have kept it in memory.
Another thing to check is background app refresh in Settings>General. If your device is like mine, almost every app has background refresh active. Think about which apps really need this feature. Probably apps associated with your home security, but maybe not HDTV, GarageBand, etc. If you need to disable Background refresh, there's a switch at the top of the page to disable for all apps.
Finally, if you’ve installed an app that automatically force closes other apps when you exit them, you should probably remove it. Certainly, I don’t advise paying for such apps.