Question

While trying to express $7^3$ as the sum of consecutive odd numbers, what is the number, $7^3$ should be divided by to find the middle number?

• A. 47, 49
• B. 47, 51
• C. 7
• D. 49

Answer 1

The correct option is C

7

To find the middle number in the series of consecutive odd numbers whose sum gives $n^3$, we divide $n^3$ by 'n'.
The sum of 7 consecutive odd numbers gives $7^3$.
To find the odd numbers whose sum is $7^3$, we first divide $7^3$ by 7.
$\Rightarrow \frac{7^3}{7}=7^2=49$
Since, 49 is an odd number it is the middle number of the series.