What is the largest three-digit number in the arithmetic sequence 1,4,7,10,13, 16, ...?

An arithmetic sequence 2,5,8, 11, 14,... is written in order in a book, one hundred numbers per page, beginning on page one. On which page will the number 11,111 appear?

Guest Jan 28, 2019

#1**+1 **

What is the largest three-digit number in the arithmetic sequence 1,4,7,10,13, 16, ...?

The common difference is 3

So....we'd like to solve this

1 + 3(n - 1) < 1000

3(n - 1) < 999

n - 1 < 333

n < 334

So....n = 333

So...the largest three-digit term is

1 + 3 ( 333 - 1) =

1 + 3(332) =

997

CPhill Jan 29, 2019

#2**+1 **

An arithmetic sequence 2,5,8, 11, 14,... is written in order in a book, one hundred numbers per page, beginning on page one. On which page will the number 11,111 appear?

The common difference is 3

So....we want to find what term 11,111 might be

11,111 = 2 + 3(n - 1) subtract 2 from both sides

11,109 = 3(n - 1) divide both sides by 3

3703 = n - 1 add 1 to both sides

3704 = n

So 11,111 will appear on page = ceiling [ 3704/100] = page 38

CPhill Jan 29, 2019