Use an arithmetic sequence to find the number of multiples of 6 between 41 and 523. justify your reasoning.

The number of multiples of 6 between 41 and 523 = 81

Step-by-step explanation:

We need to find multiples of 6 between 41 and 523.

First multiple is 42.

That is first term is 42.

Common difference is 6.

The last term less than 523 and multiple of 6 is 522.

So we need to find number of terms in

               42, 48, 54 , 60 , 66 522

           We have

                       a + (n-1) d = 522

                      42 + (n-1) 6 = 522

                       (n-1) 6 = 522 - 42 = 480

                          (n-1) = 80

                            n = 81

That is there are 81 terms in this arithmetic progression.

The number of multiples of 6 between 41 and 523 = 81

42

step-by-step explanation: