[tex]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} = 16\cdot 11\Rightarrow S_{11}=176 [/tex]
