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

n (n - 1) + 1

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n (n + 1) + 1

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(n - 1) (n + 2) + 1

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(n - 1) (n + 1) + 1

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Solution

The correct option is C $(n - 1) (n + 2) + 1$
Number of term required in $n^{3}$ is $n$ and all are consecutive odd numbers.
Hence, the first term is $n (n - 1) + 1$ and common difference between two consecutive odd numbers is $2$ .
So using arithmetic progression, the last term will be $(n - 1) (n + 2) + 1$ .

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