Question

$9^3$ can be represented as a sum of how many consecutive odd number?

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

Answer: (A)

9

For any natural number (n), n${}^3$ can be represented as sum of 'n' consecutive odd natural numbers with 'n${}^2$' being their mean.

$\therefore$ 9${}^3$ can be represented as a sum of 9 consecutive odd numbers and the numbers are 73, 75, 77, 79, 81, 83, 85, 87, 89.
i.e., 73+75+77+79+81+83+85+87+89 = 729 = 9${}^3$