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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?

 Jan 28, 2019
 #1
avatar+102372 
+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

 

 

cool cool cool

 Jan 29, 2019
 #2
avatar+102372 
+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 

 

 

cool cool cool

 Jan 29, 2019

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