Question

5+10+15+20+25+....+100

Answer 1

     [tex]-Dam~factor~comun~pe~5~si~avem:\\ 5(1+2+3+4+5+...+20)\\ -Avem~o~suma~Gauss~aplicam~formula:[n(n+1)]:2\\ =\ \textgreater \ 5*\frac{20*21}{2} =\ \textgreater \ 5*10*21=\ \textgreater \ 50*21=\ \textgreater \ 1050\\\\ S_n=5+10+15+20+25+...+100\\ S_n=5(1+2+3+4+5+...+20)\\ S_n=5*10*21\\ S_n=50*21\\ S_n=1050[/tex]

Answer 2

Progresie aritmetica : primul termen 5, ultimul 100, 20 elemente
S=[(5+100)/2]*20=105*10=1050
sau
S=5*(1+2+3+....+20)=5*{[(1+20)/2]*20}=5*210=1050