inter vlan routing and access switch default gateway

I have a question. If we have 5 2960 layer 2 switches with vlans 2,3,4,5,6 that they are connected via trunk port to 3850 and we've created vlans(2,3,4,5,6) on 3850 and gave them an ip each in it's vlan range. They all need to ping each other. does we need to set default gateway on 2960 to it's vlan ip on 3850? or we just need to set that IP on clients in each vlan? If we make vlan 1 as management does we need to set a default gateway for it? Thank you in advance