The sum of 1 + 3 + 5 + 7 + dots up to n terms | vedclass

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(C) The given series is $1, 3, 5, 7, \dots$ which is an Arithmetic Progression $(AP)$ with first term $a = 1$ and common difference $d = 3 - 1 = 2$.Th

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$n^2$

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(C) The given series is $1, 3, 5, 7, \dots$ which is an Arithmetic Progression $(AP)$ with first term $a = 1$ and common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms of an $AP$ is given by the formula $S_n = \frac{n}{2} \{2a + (n - 1)d\}$.Substituting the values $a = 1$ and $d = 2$:$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$.

The sum of $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is

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