Learn Finnish: Suomessa minä totun kylmään ilmastoon ja uuteen arkeen. - In Finland I get used to the cold climate and the new everyday life.

This is because of the verb tottua (to get used to). In Finnish, certain verbs demand a specific case for the words connected to them, which is called verb rection. Tottua always requires the illative case. You can think of it as adapting or settling "into" a new situation. Because of this rule, both the adjectives and the nouns take the illative endings, giving us kylmään ilmastoon and uuteen arkeen.

The dictionary form of "to get used to" is tottua. Why is it spelled with only one "t" in totun?

This is a classic example of consonant gradation. The dictionary form tottua has a strong double -tt-. However, when you add the -n ending to say "I get used to", you close the syllable (to-tun). This closed syllable weakens the double -tt- to a single -t-.

The word for "new" is uusi. Why does it change so drastically to uuteen?

Words ending in -si, like uusi (new) and vuosi (year), belong to a special group. Before adding most case endings, the -si changes to a -te- stem. To make the illative case, you lengthen the final vowel of that stem and add -n. Therefore, the stem uute- becomes uuteen.

Why does arki (everyday life) become arkeen instead of "arkiin"?