Question

A mathematics book contains 20 pages. one sheet is missing among them. sum of the page numbers of the remaining pages of the mathematics book is 195. the numbers written on both the sides of the missing sheet of the mathematics book must be

Answer 1

Sum of n numbers in an arithmetic progression = n/2*( 1st term + last term )

Hope this helps.

Answer 2

Given:

The book has 20 pages.

One sheet is missing.

Sum of all remaining page numbers is 195.

To Find:

The page numbers of the missing sheet.

Formula:

$S_n = \dfrac{n}{2 }(2a + (n - 1)d)$

Find the sum of all the number pages in a 20 pages book:

$S_n = \dfrac{n}{2 }(2a + (n - 1)d)$

$S_{20} = \dfrac{20}{2 }(2(1) + ((20) - 1)1)$

$S_{20} = 210$

Find the sum of the the two missing page numbers:

Sum of the page numbers of a 20 pages book = 210

Sum of the page numbers of the book with the missing sheet = 195

Sum of the two missing page numbers = 210 - 195

Sum of the two missing page numbers = 15

Find the missing page numbers:

The two numbers must be consecutive.

Let one page be x and the other page is (x + 1)

x + (x + 1) = 15

x + x + 1 = 15

2x + 1 = 15

2x = 14

x = 7

One page = x

One page = 7

Other page = x + 1

Other page = 7 + 1

Other page = 8

Answer: The two missing page numbers are 7 and 8.