Respuesta :

[tex]a_1=3\\a_2=3+1=4\ (a_1+1)\\a_3=4+1=5\ (a_2+1)\\a_4=5+1=6\ (a_3+1)\\a_5=6+1=7\ (a_4+1)\\\\it's\ an\ arithmetic\ sequence\ where\ a_1=3\ and\ d=1\\\\formula\ for\ the\ sum\ of\ the\ first\ n\ terms:\ S_n=\frac{2a_1+(n-1)d}{2}\cdot n\\\\therefore\\\\S_n=\frac{2\cdot3+(n-1)\cdot 1}{2}\cdot n=\frac{6+n-1}{2}\cdot n=\frac{5+n}{2}\cdot n=\frac{5+n}{2}\cdot\frac{n}{1}=\boxed{\frac{5n+n^2}{2}}[/tex]

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