When your apps are open in the background, they are in a state where it is easy to re launch them. This does not mean that they are using much of your resources. Resources are accessed by apps open in the background only when a background process is involved such as uploading a file, location tracking, playing audio. In fact, closing background apps uses more battery. When you force quit an app, you are using a portion of your resources and battery for closing it and clearing it from RAM. Resources will be used when you open it again leading to increased usage of battery. To improve battery life, turn off notifications for frequently used apps, turn off vibration for calls/notifications and dim the display.
Picture Credit : Google
