For an A.P., it is given that the first term $(a) = 5$, common difference $(d) = 3$, and the $n^{th}$ term $(a_n) = 50$. Find $n$ and sum of first $n$ terms $(S_n)$ of the A.P.

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Step 1: $a_n = a + (n - 1)d \Rightarrow 50 = 5 + (n - 1) 	imes 3$
Step 2: $\Rightarrow n - 1 = 15 \Rightarrow n = 16$
Step 3: $S_n = \frac{n}{2}(a + a_n) = \frac{16}{2}(5 + 50)$
Step 4: $= 8 	imes 55 = 440$

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