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
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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
