Question

Calculati:10+15+20+25+...+315=?
12+18+24+30+...+408=?
19+38+57+76+...+665=?

Answer 1

10+15+20+25+...+315=5*(1+2+3+4++63)=5*63*64/2 -5 =10080 - 5*1= 10075

12+18+24+30+...+408=6*(1+2+3+4+5.....+68)=6*68*69/2 -6*1=2346-6=2340


19+38+57+76+...+665=19*(1+2+3+4...+35)= 19*35*36/2=11970

Answer 2

progresii aritmetice
1) cu ratia 5, avem 62 termeni(10, 10+5.1,10+5.2,10+5.3,.......,10+5.61)
S=62(10+315)/2=31.325=10.075
2) cu ratia 6, avem 67 de termeni(12+6.0, 12+6.1, 12+6.2, 12+6.3,...., 12+6.66)
S=67(12+408)/2=67.210=14.070
3) cu ratia 19, avem 35 termeni(19+19.0, 19+19.1, 19+19.2, 19+19.3,..., 19+19.34)
S=35(19+665)/2=11.970
Succes in continuare!