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(B) The first $n$ odd natural numbers form an Arithmetic Progression $(AP)$ where the first term $a = 1$ and the common difference $d = 2$.The sequenc

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$n^{2}$

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(B) The first $n$ odd natural numbers form an Arithmetic Progression $(AP)$ where the first term $a = 1$ and the common difference $d = 2$.The sequence is $1, 3, 5, \dots, (2n-1)$.The sum of an $AP$ is given by the formula $S_n = \frac{n}{2} [2a + (n-1)d]$.Substituting the values: $S_n = \frac{n}{2} [2(1) + (n-1)2]$.$S_n = \frac{n}{2} [2 + 2n - 2]$.$S_n = \frac{n}{2} [2n]$.$S_n = n^2$.Therefore,the sum of the first $n$ odd natural numbers is $n^2$.

The sum of the first $n$ odd natural numbers is $\ldots \ldots \ldots$

Similar Questions

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