How to customize individual tabs? (changing background color, indicator color and text color)

Just set your custom view at the tab creation time, something like:

final Tab firstTab = actionBar.newTab()
                              .setText(mAppSectionsPagerAdapter.getPageTitle(0))
                              .setCustomView(R.id.custom_tab_view_red);
final Tab secondTab = actionBar.newTab()
                               .setText(mAppSectionsPagerAdapter.getPageTitle(1))
                               .setCustomView(R.id.custom_tab_view_blue);
// etc

actionBar.addTab(firstTab);
actionBar.addTab(secondTab);
// etc

in inCreate().

You’ll also have to define Views corresponding to the above ids in your xml layout file (and not styles).

Or, if you want to create the view directly:

final View firstCustomView = new CustomView(this);
firstCustomView.setBackgroundColor(Color.BLUE);  // or with drawable or resource
final Tab firstTab = actionBar.newTab()
                              .setText(mAppSectionsPagerAdapter.getPageTitle(0))
                              .setCustomView(firstCustomView);
actionBar.addTab(firstTab);
// then same for other tabs, just with another color

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Leaving the below information for reference:

To define one such view, you need to specify it an Android Context. This is usually the Activity where the tabs will be displayed.
Supposing that you initialize your tabs in an Activity, simply pass the Activity instance as a Context:

ctv = new CustomView(this, R.attr.tabStyleAttr);

if from inside the Activity, or for example:

ctv = new CustomView(getActivity(), R.attr.tabStyleAttr);

if from inside a Fragment, etc.

As for setting a specific style for action bar tabs, no need to go create a custom view programmatically as you’re trying to. Read up a little about the action bar first, then check the example they provide. As you can see, you’ll be able to specify the tab style in xml:

In your manifest file, you can apply the theme to your entire app:

<application android:theme="@style/CustomActionBarTheme" ... />

Or to individual activities:

<activity android:theme="@style/CustomActionBarTheme" ... />

for example.

For a complete example matching perfectly your use case, see this Android doc article: https://developer.android.com/training/basics/actionbar/styling.html#CustomTabs . Notice the usage of state-lists to achieve the “when selected style”.