Question

Determinati nr natural x din egalitatea:


2+7+12+...+x=1550

progresie aritmetica fact =)
Thx.

Answer 1

Răspuns

Explicație pas cu pas:

2+7+12+...+x=1550    x=2+m×5

2+2+5+2+5×2+...2+m×5=1550

2(m+1)+5(1+2+....+m)=1550

2m+2+5×m(m+1)/2=1550

4m+4+5m²+5m=3100

5m²+9m-3096=0

Δ=9²-4×5×(-3096)=81+61920=62001

m₁=(-9+√62001)/(2×5)=(-9+249)/10=240/10=24

m₁=(-9-√62001)/(2×5)=(-9-249)/10=258/10∉N

⇒x=2+m×5=2+24×5=2+120=122