Answer
$${S_{60}} = 3660$$
Work Step by Step
$$\eqalign{
& {\text{The first 6}}0{\text{ positive even integers form the arithmetic sequence }} \cr
& 2,4,6,8,10,{\text{ }}.{\text{ }}.{\text{ }}.{\text{ }}, \cr
& {a_1} = 2,\,\,\,\,d = 2,\,\,\,n = 60 \cr
& {\text{The formula of the sequence is}} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {a_{60}} = 2 + \left( {60 - 1} \right)\left( 2 \right) \cr
& {a_{60}} = 120 \cr
& \cr
& {\text{Let }}{a_1} = 2,\,\,{a_{60}} = 120,\,\,n = 60 \cr
& {\text{Using the formula }}{S_n} = \frac{n}{2}\left( {{a_1} + {a_n}} \right) \cr
& {S_{60}} = \frac{{60}}{2}\left( {2 + 120} \right) \cr
& {S_{60}} = 30\left( {122} \right) \cr
& {S_{60}} = 3660 \cr} $$