R. Peary was . . . . . . . . famous American polar traveler. He was . . . . . . . . first to reach . . . . . . . . North Pole in 1909.

In the first blank, article "a" will be used as it is written 'American Polar Traveller' and it is a general noun.
In the second blank, article "the" will be used because article "the" is used when with ordinals such as "first", "second" etc and it is given that 'he was () first to reach.'
Similarly, 'North Pole' is a proper noun (something unique). Therefore, in the third blank, article "the" will be used.