Question

CALCULATI:
5+10+15+___+45=
3+6+9____+120=

Answer 1

5+10+15+...+45=5(*1+2+3+...+9)=5*9*10:2=225
3+6+9+...+120=3(1+2+3+...+40)=3*40*41:2=2460

Answer 2

$\displaystyle a).5+10+15+...+45= 5(1+2+3+...+9)=5 \times \frac{9(9+1)}{2} = \\ \\ =5 \times \frac{9 \times 10}{2} =5 \times \frac{90}{2} =5 \times 45=225 \\ \\ b).3+6+9+...+120=3(1+2+3+...+40)=3 \times \frac{40(40+1)}{2} = \\ \\ =3 \times \frac{40 \times 41}{2} =3 \times \frac{1640}{2} =3 \times 820=2460$