Sum modulo 10 - Part 1

My method of working goes as follows:

$a_0 + a_1 + \ldots + a_9 = 35$ ,

$a_{10} + a_{11} + \ldots + a_{19} = 35$ ,

$a_{20} + a_{21} + \ldots + a_{29} = 35$ ,

$a_{30} + a_{31} + \ldots + a_{39} = 35$ and so on.

Observe that $2015 = 57 * 35 + 20$

From the pattern mentioned above, it is easy to note that $a_0 + a_1 + \ldots + a_{569} = 57 * 35$

$a_0 + a_1 + \ldots + a_{569} + a_{570} + a_{571} + a_{572} + a_{573} = 57 * 35 + 5 + 6 + 8 + 1 = 2015$

So $k = 573$