Question

the sum of five consecutive odd numbers is 6785. what is the difference between the greatest and the smallest of these numbers

Answer 1

$<b>{The sum of five consecutive odd number is 6785. What is the difference between the greatest and the smallest of these numbers?$

The 5 odd no's are in A.P

2n+1, 2n+3, 2n+5, 2n+7, 2n+9

According to the question

2n+1+…….+ 2n+9= 6785

10n + 25= 6785

10n= 6785–25 = 6760

n= 6760/10 = 676 . Now greatest number is 2n +9 = 2(676) + 9= 1361

Smallest number is 2n+1= 2(676) +1 = 1353

$\boxed{Greatest number - Smallest number = 1361–1353= 8}$