Question

S=2+9+16+23.....+2018este divizibila cu 10

Answer 1

   

$\displaystyle\\\text{{\bf Pasul 1:}~~Verificam daca ultimul termen (2018) face parte din sir.}\\\\\text{Termenul general}=7k+2,k\in N\\\\2018=2016+2=7\times288+2\\\\\implies~~2018\text{ apartine sirului.}\\\\\text{{\bf Pasul 2:}~~Calculam numarul de termeni n.}\\\\n=\frac{2018-2}{7}+1=\frac{2016}{7}+1=288+1=289~\text{ de termeni}\\\\\text{{\bf Pasul 3:}~~Calculam suma S.}\\\\S=\frac{289(2018+2)}{2}=\frac{289 \times 2020}{2}=289\times1010 =\boxed{\bf(289\times101\times10)~\vdots~10}$