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