Its an AP series
Sum of series is given by
Sn=$\frac{n}{2}\left \{ 2a+(n-1)d \right \}$
300=$\frac{15}{2}\left \{ 2a+(15-1)2 \right \}$
a=6
so at first day man started eating 6 mangos
at 3rd day number of mangoes eaten is
t3=6+(3-1)*2
t3=10
He ate 10 mangoes on 3rd day