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?
+128407 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
+128407 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
