Question

Sa se rezolve ecuatia 3+5+7+.....+x=120​

Answer 1

$3+5+7+...+x=120$

$S_n=\frac{(a_1+a_n)n}{2} =\frac{(3+x)\cdot\frac{x-1}{2} }{2} =120 \\\\Sirul \ 3+5+7+...+x \ are \ \frac{x-3}{2}+1=\frac{x-1}{2} \ termeni.$

$\frac{(3+x)(x-1)}{4} =120\\3x-3+x^2-x=480\\x^2+2x-483=0$

$\Delta=4+4\cdot483=44^2\\x_{1,2}=\frac{-2 \pm 44}{2} =21,\ -23$

$Cum \ x > 0 \implies \framebox {x=21}$