# 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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