Question

The sum of three consecutive odd numbers is 75. Which is the largest among them?

Answer 1

Given sum of three consecutive odd numbers is 75

Odd numbers are 1, 3, 5, 7, 9, 11, 13

∴ The difference between 2 consecutive odd numbers is always 2. or in other words, if one odd number is x, the next odd number would be x + 2 and the next number would be x + 2 + 2x + 4

i.e x + 4

Since sum of 3 consecutive odd numbers is 75

∴ x + x + 2 + x + 4 = 75

∴ 3x + 6 = 75

⇒ 3x = 75 – 6

∴ 3x = 69

x = `69/3` = 23

∴ The odd numbers are 23, 23 + 2, 23 + 4

i.e 23, 25, 27

∴ Largest number is 27.