What is the remainder when the sum 1 + 7 + 13 + 19 + ... + 253 + 259 + 265 + 271 is divided by 6?
7 - 1 ==6 - this is the common difference.
Your sequence looks like this:
1 , 7 , 13 , 19 , 25 , 31 , 37 , 43 , 49 , 55 , 61 , 67 , 73 , 79 , 85 , 91 , 97 , 103 , 109 , 115 , 121 , 127 , 133 , 139 , 145 , 151 , 157 , 163 , 169 , 175 , 181 , 187 , 193 , 199 , 205 , 211 , 217 , 223 , 229 , 235 , 241 , 247 , 253 , 259 , 265 , 271 , >>Number of terms = 46>>Total Sum == 6256
6256 mod 6 ==4 - the remainder.
