Question

Determine a soma dos 50 primeiros múltiplos naturais positivos de 5

Answer 1

Sn = M.n.( n + 1 ) / 2
S50 = 5 . 50 . ( 50 + 1 ) / 2 
S50 = 250 . ( 51 ) / 2 
S50 = 12750  / 2 
S50 = 6375

Answer 2

$\mathrm{O\ 1\º\ m\acute{u}ltiplo\ natural\ de\ 5\ \acute{e}\ o\ pr\acute{o}prio\ 5.}\\\\ \mathrm{O\ 50\º\ m\acute{u}ltiplo\ natural\ de\ 5\ \acute{e}\ 50*5=250.}\\\\ \mathrm{Temos\ uma\ P.A.\ com\ 1\º\ termo\ a_1=5\ e\ 50\º\ termo\ a_{50}=250.}\\\\ \mathrm{Pela\ soma\ dos\ termos\ de\ uma\ P.A.,\ para\ n=50,\ teremos}\ \textrm{que:}\\\\ \mathrm{S_n=\dfrac{n}{2}(a_1+a_n)\ \to\ S_{50}=\dfrac{50}{2}(a_1+a_{50})\ \to}\\\\ \mathrm{\to\ S_{50}=25(5+250)\ \to\ \boxed{\mathbf{S_{50}=6375}}}$