5 + 12 + 19 + 26 + 33 + .................... + 705 = 35 855
→ stabilesc cati termeni are suma, cu ratia 7 ( 12 - 5 = 7; 19 - 12 = 7 ; ........ )
( 705 - 5 ) : 7 + 1 = 700 : 7 + 1 = 100 + 1 = 101 termeni are suma
→ aplic formula sumei lui Gauss
= 101 × ( 5 + 705 ) / 2 =
= 101 × 710 / 2 =
= 101 × 355 =
= 35 855