3 + 5 + 7 + .......To N Term

Sol:

\( S_{n} = 3 + 5 + 7 + …..n\)

Since above series is an AP with a = 3

d = 5 – 3 = 2

Therefore,

\( S_{n} = \frac{n}{2} [2a + (n – 1)d]\) \( \Rightarrow \frac{n}{2} [2 * 3 + (n – 1)2]\) \( \Rightarrow \frac{n}{2} [6 + 2n – 2]\) \( \Rightarrow \frac{n}{2} [2n + 4]\) \( \Rightarrow n (n + 2)\)

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