می‌دانيم جملهٔ $n$‌ام یک دنباله‌ی حسابی از رابطه‌ی ${{t}_{n}}={{t}_{1}}+(n-1)d$ بدست می‌آید، پس: $\left\{ \begin{matrix}{{t}_{12}}+{{t}_{10}}=5  \\{{t}_{12}}+{{t}_{10}}=25  \\\end{matrix} \right.\,\,\Rightarrow \left\{ \begin{matrix}({{t}_{1}}+11d)-({{t}_{1}}+9d)=5  \\({{t}_{1}}+11d)-({{t}_{1}}+9d)=25  \\\end{matrix} \right.$ بنابراین: $\Rightarrow \left\{ \begin{matrix}2d=5\Rightarrow d=2/5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,  \\2{{t}_{1}}+20d=25\xrightarrow{d=2/5}2{{t}_{1}}+20\times (2/5)=25  \\\Rightarrow {{t}_{1}}=-12/5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,  \\\end{matrix} \right.$ پس جملهٔ بيست و يكم برابر است با: ${{t}_{21}}={{t}_{1}}+20d=-12/5+20\times (2/5)=37/5$