Final answer:
Germany offering Austria a 'blank check' gave Austria-Hungary unconditional support, leading to their aggressive actions and the start of World War I.
Step-by-step explanation:
The consequence of Germany offering Austria a 'blank check' was that it gave Austria-Hungary the assurance of unconditional support from Germany, which emboldened Austria-Hungary to take aggressive actions. With Germany's backing, Austria-Hungary declared war on Serbia, leading to a chain of events that ultimately triggered the start of World War I. This support from Germany allowed Austria-Hungary to pursue its imperialist ambitions and escalate the conflict in the Balkans.