Of which Chomsky-type is the language $L = \{a^jb^ic^{2i} | i,j \in \mathbb{N}^0\}$?
The language is context-free. You can use the pumping lemma for regular languages to show that it is not regular. However, you can construct a context-free grammar to show that the language is context free. For example, the following CFG grammar would generate it

$S \to A\ |\ aS  $

$A \to \epsilon\ |b A cc $