My Angular 2 application needs a higher version than 3.9.x of NPM, but the default version which is getting installed is 3.5.2 using
sudo apt-get install npm
You're getting version 3.5.2 of npm, because that's the version in the repositories. Debian and Ubuntu are typically terrible at keeping up with Node and npm's fast rate of development, so you'll often find the packages are out of date, and aren't much use to you.
Instead, follow the instructions given on the Node.js website:
Node.js is available from the NodeSource Debian and Ubuntu binary distributions repository (formerly Chris Lea's Launchpad PPA). Support for this repository, along with its scripts, can be found on GitHub at nodesource/distributions.
NOTE: If you are using Ubuntu Precise or Debian Wheezy, you might want to read about running Node.js >= 6.x on older distros.
curl -sL https://deb.nodesource.com/setup_6.x | sudo -E bash - sudo apt-get install -y nodejs
Alternatively, for Node.js v7:
curl -sL https://deb.nodesource.com/setup_7.x | sudo -E bash - sudo apt-get install -y nodejs
nodejs package provided by NodeSource includes npm. Simply install that, and you'll be ready to go with the latest version.