Answer
$${a_1} = - 10,\,\,\,\,d = 3$$
Work Step by Step
$$\eqalign{
& {S_{25}} = 650,\,\,\,{a_{25}} = 62 \cr
& {\text{Use the first formula for }}{S_n} \cr
& {S_n} = \frac{n}{2}\left( {{a_1} + {a_n}} \right) \cr
& {\text{Let }}n = 25 \cr
& {S_{25}} = \frac{{25}}{2}\left( {{a_1} + {a_{25}}} \right) \cr
& 650 = \frac{{25}}{2}\left( {{a_1} + 62} \right) \cr
& {\text{Solve for }}{a_1} \cr
& 52 = {a_1} + 62 \cr
& {a_1} = - 10 \cr
& \cr
& {\text{Now find }}d,{\text{ use the formula for the }}n{\text{th term}} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {a_{25}} = {a_1} + \left( {25 - 1} \right)d \cr
& 62 = - 10 + \left( {24} \right)d \cr
& 72 = 24d \cr
& d = 3 \cr
& \cr
& {\text{Then,}} \cr
& {a_1} = - 10,\,\,\,\,d = 3 \cr} $$
