Is it possible to upgrade Apache Cassandra 2.1.9+ to Apache Cassandra 3.1+ directly?
The release notes for 3.0 mention direct upgrades need a minimum of Apache Cassandra
Yes, you can upgrade from Cassandra 2.1.9 (or higher) to Cassandra 3.1 (or higher).
As stated in the DataStax dev blog in June of 2015, Cassandra moved to a "tick-tock" release cycle with version 3. The details of which you can get from the link, but the main point is that the release structure of 3.x is not the same as it was with 2.x.
Cassandra 2.0, 2.1, and 2.2 were different enough in terms of features and storage modifications that they required a structured upgrade path. Cassandra 3.x does not. You can upgrade directly to 3.1, 3.4, or 3.10 (just released). As long as you meet the 3.0 upgrade requirements (Cassandra version >= 2.1.9) you don't need to worry about intermediate upgrades with the 3.x line.
When upgrading from 2.2.8 to 3.11.6 , while upgrading the last node in the cluster, when last node on which the upgrade is left the client is not able to connect to cluster untill upgrade on the last node finishes. We are having a 5 node cassandra cluster running on aws ec2.
As per my experience about upgrading Cassandra if you are doing upgrade from below 2.1.9 then you must upgrade to 2.1.9 or above then you can directly upgrade to 3.x version. There is no issue in this way and you upgrade will be successful but if you are doing it on production make sure to do rolling upgrade with all prerequisites and backup. Don't forget to run nodetool upgradesstables after Cassandra upgrade.