[tex]\text{First term, a} = \dfrac 12\\\\T_{22} = 10\\\\\implies a + (22-1) d = 10\\\\\implies \dfrac 12 + 21d =10 \\\\\\\implies \dfrac{1+42d}2 =10\\\\\implies 1+ 42 d = 20 \\\\\implies 42d = 19 \implies d = \dfrac{19}{42}\\\\\text{nth term ,}~\\ T_n =a +(n- 1)d = \dfrac 12 + (n-1)\dfrac{19}{42}=\dfrac 12 \left[1 + (n-1)\dfrac{19}{21}\right][/tex]
