Question

2+4+6+...+100=? 

3+7+11+15+...+43=?

Answer 1

S=2+4+6+...+100
S=100+98+96+...+2
(le aduni)
2S=102+102+102+...+102

Afli termenii: (ultimul-primul):din cat in cat merge+1
(100-2):2+1=
98:2+1=
49+1=
50

2S=102x50
2S=5100/:2
S=2550

asa sa faci si la cealalta

Answer 2

2+4+6+...+100=?
2(1+2+3+....+50) = 
Se face Gauss in paranteza
2* 50*51/2   2 cu 2 se simplifica si rez va fi 
50*51=2550

 3+7+11+15+...+43=?  d=4(ca e din 4 in patru)

Sn = n(a1+an)/2
Adica
S43 =43(3+an)/2

an=a1+(n-1)*d
a43 = 3+ (43-1)*4
a43 = 3+42*4
a43=3+168
a43=171

Inlocuim:
S43 = 43*(3+171)/2
S43 = 43*174/2 
S43=3741