Question

If we write $n^3$ as the sum of consecutive odd numbers, then what will be the first term?

• A. $2n+1$
• B. $(2n+1)(2n-1)$
• C. $2n-1$
• D. $n(n-1)+1$

Answer 1

The correct option is D $n(n-1)+1$

From observation $1^3=1;1\times 0+1$, where $n=0$.
$2^3=3+5;3=2\times 1+1$, where $n=2$.
$3^3=7+9+11;7=3\times 2+1$, where $n=3$.

Similarly, for $n^3$, the first term will be $n(n-1)+1$.

Therefore, option $D$ is correct.