If the sum of first $6$ terms of an A.P. is $36$ and that of the first $16$ terms is $256$, find the sum of first $10$ terms.

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Step 1: $S_6 = 36 \Rightarrow \frac{6}{2}[2a + 5d] = 36 \Rightarrow 2a + 5d = 12$ ... (1)
Step 2: $S_{16} = 256 \Rightarrow \frac{16}{2}[2a + 15d] = 256 \Rightarrow 2a + 15d = 32$ ... (2)
Step 3: Solving (1) and (2): $10d = 20 \Rightarrow d = 2$, $a = 1$.
Step 4: $S_{10} = \frac{10}{2}[2(1) + 9(2)] = 5 	imes 20 = 100$.

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