ข้อสอบคณิต O-NET - 2549

$$\begin{gathered} \mathrm{จากโจทย์}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{S}_n = 3n^2+2 \\ \mathrm{จะได้} S_{10} = a_1+a_2+a_3+\dots +a_9+a_{10} \\ S_9 = a_1+a_2+a_3+\dots +a_9 \\ \mathrm{ดังนั้น} a_{10} = S_{10}-S_9 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} S_{10} = 3{\left(10\right)}^2+2 \\ = 302 \\ S_9 = 3{\left(9\right)}^2+2 \\ = 245 \\ \mathrm{ดังนั้น} a_{10} = 302-245 \\ = 57 \\ \mathrm{ดังนั้น} \mathrm{ตอบข้อ} 1 \end{gathered}$$