If the sum of m consecutive odd integers is $m^{4}$ , then the first integer term is

m^{3} - m - 1

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m^{3} - m + 1

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m^{3} + m - 1

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\frac{2 m^{3} - m + 1}{2}

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Solution

The correct option is C $m^{3} - m + 1$
The $m$ consecutive terms is an A.P. with its first term being $a$ and common difference being 2.
$\Rightarrow m^{4} = \frac{m}{2} [2 a + (m - 1) \times 2]$
$m^{4} = m (a + m - 1)$
$m^{3} - m + 1 = a$

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