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/dev/sda1 (20GB) Linux
/dev/sda2 (1GB) extended
/dev/sda5 (1GB) Swap
I have upgraded my virtual disk, so now /dev/sda has 30GB. The additional 10GB are unassigned and I want them to be an extension to /dev/sda1. The partitions are already one after another...
I do not think that the OP's request has anything to do with changing the size of a disk while in use. The disk has already been extended.
The OP has several options.
1) Use Gparted on a live system to move the extended partition and the swap and extend the root partition.
2) From the installed system, disable the swap with "swapoff -a" and use Gparted as above. An ext4 partition in use can be extended online.
3) From the installed system, disable the swap as above, and use your favourite partitioning tool to delete the swap partition and the extented partition, extend the root partition and its filesystem, create a new swap partition and format it with mkswap -U same-uuid-as-before-in-fstab.
Final note : the use of LVM instead of plain partitions would have made this much easier. No need to move logical volumes around to extend another volume.