I'm sorry, maybe it's written somewhere, Unfortunately I couldn't find the answer. I need to upgrade the Moodle server from version 3.7.2+ (Linux CentOS). I have read the documentation, discussions on the internet. If I understand correctly, Moodle in this version cannot be immediately converted to the latest version, but do I have to upgrade the individual main versions gradually with respect to the PHP and DB versions? Please, is that so? Or is there another more suitable way. Thank you.
In reply to David Jedziniak
Re: Upgrade the Moodle server from version 3.7.2+
by Visvanath Ratnaweera -
You are right. You can't go from 3.7 to the latest, which is 4.2. But you don't have to march it through every major version (3.7 > 3.8 > 3.9..) either. Usually there are more than one solution which you can find in the chart http://www.syndrega.ch/blog/#php-and-dbms-compatibility-of-major-moodle-releases.
From 3.7.2 I prefer > 3.7.last > 3.9 (LTS) > 4.1 (LTS).
You might explore carefully whether you need 4.2. It needs higher system software and live shorter than 4.1 which is LTS. Ref https://moodledev.io/general/releases.
For each step there is an Upgrading document page.
Mr. V is correct ... some more however ....
Since you are on CentOS 7 there are things that you should do prior to the 'march' and could do to ease the pain of the 'march'.
Should do prior: get a list of addons you have currently installed and research if those addons have a version for destination version of core. Is your site using a addon theme? Best, for the march to force the use of boost until you reach destination version.
There are repos for PHP and for MySQL that you could use which make doing those upgrades much easier.
There is also a 'better way' to upgrade core code via git. All command line but CentOS does have ssh.
One could acquire new code and upgrade with CLI scripts that exist in code/admin/cli/ - no FTP needed ... and less prone to human error as well.
'SoS', Ken
Thank you very much. I wanted to migrate the running Moodle to a server with the latest stable version of Linux and prepare scripts for subsequent updates using GIT. Unfortunately, I found out that it's not just about installing a new version with restoring backups. Until now, I only knew Moodle as "student" 
. Thanks to this, I will get to know Moodle better at the administrator level .
David