~ていく
A change continues from now onward
You'll be able to describe an action moving away or a change that develops into the future.

蓮は学校へ歩いていきます。
ren wa gakkou e aruite ikimasu.
What do you think this sentence means?
Ren walks away toward school.
Move away or continue from now on
~ていく describes movement away from the viewpoint, or a process continuing into the future. The directional idea applies to both space and time.
これからもっと寒くなっていきます。
kore kara motto samuku natte ikimasu.
It will get colder from now on.
Form and use ~ていく
Use いきます for politeness. In movement examples identify where the speaker is; for continued change, the viewpoint is now and the process extends onward.
これからもっと寒くなっていきます。
kore kara motto samuku natte ikimasu.
It will get colder from now on.
日本語の勉強を続けていきます。
nihongo no benkyou o tsuzukete ikimasu.
I will keep studying Japanese from now on.
A change reaching now or continuing from now
~てくる traces a change up to the present; ~ていく traces it forward from the present. Both can describe the same kind of gradual change.
~てくる
最近、日が長くなってきました。
saikin, hi ga nagaku natte kimashita.
The days have been getting longer lately.
The change has developed up to now.
~ていく
これから、日が長くなっていきます。
kore kara, hi ga nagaku natte ikimasu.
The days will get longer from now on.
The change continues from now into the future.
これから、日本に住む外国人は増えていくでしょう。
korekara, nihon ni sumu gaikokujin wa fuete iku deshou.
From now on, the number of foreigners living in Japan will probably keep increasing.
雨の予報ですから、かさを持っていったほうがいいですよ。
ame no yohou desu kara, kasa o motte itta hou ga ii desu yo.
Rain is forecast, so you'd better take an umbrella with you.
友だちの家にケーキを買っていきます。
tomodachi no ie ni keeki o katte ikimasu.
I'll buy a cake and take it to my friend's house.
7 more examples in the grammar path — free for a limited time.