Question

1. Calculati sumele
a) 5+10+15+20+........+1000
b) 11+22+33+44+.........+7700
c)15+30+45+60+........+600

2. Daca a+b=20 si b+c=30 calculati
3×a+7×b+4×c

3. Stiind ca x+3×y=2×y+z=14 calculati
5×x+11×y-2×z=

Answer 1

1. Calculati sumele:

a)5+10+15+.....+1000=5(1+2+3+...+200)=5*200*201/2=5*201*100=1005*100=100500

b)11+22+33+...+7700=11(1+2+3+...+700)=11*700*701/2=11*701*100=7711*100=771100

c)15+30+45+...+600=15(1+2+3+...+40)=15*40*41/2=15*41*20=615*2*10=1230*10=12300

2. Daca a+b=20 si b+c=30 calculati  3×a+7×b+4×c

20+20+20+30+30+30+30=180

3a+7b+4c=180

33+33+33+11+11=99+22=121

5a+3b+2b=121

3. Stiind ca x+3×y=2×y+z=14 calculati 5×x+11×y-2×z

5 x + 11y - 2 z =  

= 5 x + 15 y - 4 y - 2 z =  

= 5 ( x + 3y ) - 2 ( 2 y + z) =

=5 × 14 - 2 × 14 =

=  70 - 28 =  

= 42