[latex]S = 1+4+7+...+31 a_1=1,quad r = 3 ,quad a_n = 31, quad \ \ a_n = a_1+(n-1)cdotr Rightarrow 31 = 1 + (n-1)cdot3 Rightarrow 3n-3+1=31 Rightarrow \ Rightarrow 3n=33 Rightarrow n=11 \ \ Rightarrow S_{11} = frac{(a_1+a_{11})cdot 11}{2} Rightarrow S_{11} = frac{(1+31)cdot 11}{2} Rightarrow S_{11} = 16cdot 11Rightarrow S_{11}=176 [/latex]