Question

Calculati:
A) 4+9+14+19+.........+204=?
B)1+4+7+10+........+100=?
C)3+6+9+.........+406=?
Va rog eu mult ... Ajutatima...

Answer 1

a)4+9+14+19+...+204=
4+4+5+4+5*2+4+5*3+...+4+5*40=
41*4+5(1+2+3+...+40)=
41*4+5*41*40/2=
41*4+100*41=
41(100+4)=41*104=4264
b)1+4+7+...+100=
1+1+3+1+3*2+...+1+3*33=
34+3(1+2+3+4...+33)=
34+3*33*34/2=
34+99*17=
34+1683=1717
c)3+6+9+....+405=
3(1+2+3+...+135)=
3*135*136/2=
3*135*68=27540

Answer 2

1) 4 + 9 + 14 + 19 + .....+204 = 
n = ( 204 - 4 ) : ( 9 - 4) +1 =
n = 200 : 5 +1 
n = 40 +1
n = 41
S = [( 204 +4 ) × 41 ] : 2 =
S = ( 208 × 41) : 2 =
S = 832 : 2
S = 416.

2) 1 +4 +7 + 10 +..........+100 =
n = ( 100 - 1 ) : ( 4 - 1) +1 =
n = 99 : 3 +1
n = 33 +1
n = 34.
S = [( 100 +1) × 34 ] : 2 =
S = ( 101 × 34 ) : 2
S = 3434 : 2
S = 1717.

3) 3 +6 +9 + ........405 =
n = ( 405 - 3) : ( 6 - 3 ) +1=
n = 405 : 3 +1
n = 135 + 1
n = 136
S= [( 405 +3) × 136 ]:2 =
S = ( 408 × 136 ) : 2
S = 14688 : 2
S = 7244.