TE-form + Iku
Kore kara wa samuku natte-iku yo
It will get colder (and continue to be that way) from now on
Examples
Kore kara wa mainichi hon o issatsu yonde-iku tsumori des
I intend to keep reading one book a day from now on
`Sono koro kara wa nihon no keizai tsuyoku natte-itta`
Japanese economy grew stronge (and continued that way) from that time on
Wakaranai koto o noote ni kaite-itta
I went on taking notes on things I didnt understand
Note
Examples above shows TE-form expressing action that keeps changes (go on, continue, grow on) from the point in time (described by speaker). Above are differences between present and past
The past tense examples above can be replaced with kuru (kita) with similar meaning - iku version is more impersonal and objective, while kuru version stressed that the change is going to or has involved the speaker.
Warning
Do not confuse it with TE-form + iku that expresses full meaning of verb Iku and has nothing to do with above usage of iku
Examples
Mainichi kaisha ni basu ni notte-iku
I ride a bus everyday and go to company
Ano resutoran de koohi o yonde-ikimashoo
Let's drink coffee at that restaurant and go = (and then continue on our way )