The Play Store is dependent on the Google Play Services when dealing with apps on the Android mobile device. In short, this would tell your device to update apps and introduce new settings and features to the Play Store. Thus, you must keep it updated if you want to make everything go smoothly on your smartphone or tablet.
Alternatively, you can use the Google Play Services APK file in order to install the latest update on your mobile device manually. You can do it smoothly if you read the instructions stated in this article. But, first you need to determine which Android version your phone is running.
Simply go to Settings > About Phone > Android Version. Likewise, you have to enable the Unknown Sources option on your device. Just go to Settings > Security > Unknown Sources and then toggle the switch to turn this option on.
Next thing to do is to determine which version of the Google Play Services suits your device. Each version has 3-number suffix after the hyphen. This will be the Android version, CPU architecture, and dots-per-inch (DPI).
You should be able to check the current version on your phone by heading to Settings > Apps > All Tab > Google Play Services. The first number is for the version of Android in which 0 equates to Android 4.4.4 or older, the number 2 means Android 5.0 and 5.1. Number 4 means Android 6.0 and higher, while number 7 means Android 5.0 and number 8 means Android TV.
The second number is the CPU architecture, wherein 1 is armeabi, 3 is armeabi-v7a, and 4 is arm64-v8a and 7 for x86. The third number is for the DPI of the Android device’s screen. The number 0 equals universal, 2 equals 160 dpi, 4 equals 240 dpi, 6 equals 320 dpi, and 8 equals 480 dpi.
These numbers should be useful if you want to update Google Play Services via the APK file manually.