Question

4+7+10+___+37
Dau coroana

Answer 1

S = 4 + 7 + 10 + ....... + 37

→ stabilesc cati termeni are suma cu ratia = 3 ( 7 - 4 = 3;   10 - 7 = 3;.... ) ⇔ progresie aritmetica cu ratia = 3

( 37 - 4 ) : 3 + 1 = 33 : 3 + 1 = 11 + 1 = 12 termeni are suma

→ aplic formula sumei lui Gauss

S = 12 × ( 4 + 37 ) ; 2

S = 6 × 41

S = 246

__________________________

sau:

4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 + 37 =

= ( 4 + 37 ) + ( 7 + 34 ) + ( 10 + 31 ) + ( 13 + 28 ) + ( 16 + 25 )  + ( 19 + 22 ) =

= 41 + 41 + 41 + 41 + 41 + 41 =

= 246