Series question a level maths

What does It mean it part c when it says it doesn't have an upper limit? is it because we have added an arithmetic component so can't have sm to infinity anymore?

You've got the right idea.
Basically we are adding something finite (the GS sum to infinity) by something infinite (3+3+3+...), so the sum tends to infinity.
Whichever order you add them doesn't matter*.

You can have sum to infinity, the sum just tends to infinity (note the difference between the two "infinities" - the first one refers to infinite number of terms, the second one refers to the actual value of the sum).

*Technically you can't always... kind of. Sum to infinity can act weird. But that's way out of the scope for A-Levels.