続く and 続ける: lasting rain and maintaining a habit
Read continuing events and maintained activities with durations and endpoints, and examine 続く for a path leading somewhere.
An event lasting over a period
雨が三日間続きました。 says that rain continued for three days. With 続く, read つづく, the ongoing event is the subject; a duration need not take を.
この暑さは来週まで続きそうです。 predicts that this heat looks likely to last until next week. そうです makes it an assessment, not an established future fact.
Someone maintains an activity
忙しくても、毎朝の散歩を続けています。 says that the speaker keeps up a morning walk despite being busy. 続ける, read つづける, marks the maintained activity with を.
休憩の後で、練習を続けましょう。 proposes continuing practice after a break. A brief pause does not prevent 続ける from referring to the same activity.
Where a path leads
この道は海まで続いています。 says that this road leads all the way to the sea. It describes a spatial connection rather than a long duration.
雨が続いている and 道が続いている share a form but have different subjects. Choose between temporal continuation and spatial extension according to what is described.
Does この道は海まで続いています say that the road continues endlessly from the sea?
Show the answer and why
No. It says the road extends to the sea, with 海まで marking that reach. It does not state anything about the road beyond the sea or an endless length.