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(C) The given series is an arithmetic progression with the first term $a = 1$ and the common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms

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$n^2$

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(C) The given series is an arithmetic progression with the first term $a = 1$ and the common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms of an arithmetic progression is given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values $a = 1$ and $d = 2$ into the formula:$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 the series $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is equal to:

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