Word Count : 425

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The recurrence relation is: $$ (n+1)a_n - n a_{n-1} = \frac{n}{2}, \quad a_0 = 10, \, n \ge 1 $$ Rewriting it: $$ a_n = \frac{n}{n+1} a_{n-1} + \frac{n}{2(n+1)} $$ --- Step 1: Compute first few terms manually. For $n = 1$: $$ a_1 = \frac{1}{2} a_0 + \frac{1}{2 \cdot 2} = \frac{1}{2} \cdot 10 + \frac{1}{4} = 5 + 0.25 = 5.25 $$ For $n = 2$: $$ a_2 = \frac{2}{3} a_1 + \frac{2}{2 \cdot 3} = \frac{2}{3} \cdot 5.25 + \frac{1}{3} = 3.5 ___ ___ __________ ___ __________ ________ __________ ________ _________.
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