What is the remainder when the sum 1 + 7 + 13 + 19 + ... + 253 + 259 + 265 + 271 is divided by 6?

Guest Mar 16, 2021

#1**+1 **

you can notice that you are adding 6 more to the previous number, starting with 1. if we divide each of these numbers by 6, we will always get a remainder of 1. we can subtract 1 from the last number and divide it by 6, to see how many numbers in total are in the sequence. we get (271-1)/6=270/6=45.

now that we know there are 45 digits and each of the remainders when divided by 6 is 1, we know that the remainder of the sum divided by 6 is 45/6=7 3/2=$\boxed3$

SparklingWater2 Mar 16, 2021

#2**+1 **

Terms in the series = (271 - 1) / 6 + 1 = 270 / 6 + 1 = 45 + 1 = 46 terms

Each term can be expressed as ( 1 + 6n ) where n = 0,1,2,3.....43, 44,45

And each term divided by 6 leaves a remainder of 1

So summing all the remainders we get 46

And 46 / 6 = 7 * 6 + 4 = remainder of 4

CPhill Mar 16, 2021