Write the first five terms of the sequence whose `n^(t h)`terms are : `a_n=n[(n^2+5)/4]`

Explanation

To find the first five terms of the sequence defined by the nth term \( a_n = n \left( \frac{n^2 + 5}{4} \right) \), we will calculate \( a_1, a_2, a_3, a_4, \) and \( a_5 \) by substituting \( n \) with 1, 2, 3, 4, and 5 respectively.

### Step-by-Step Solution:

1. **Calculate \( a_1 \)**:
\[ a_1 = 1 \left( \frac{1^2 + 5}{4} \right) = 1 \left( \frac{1 + 5}{4} \right) = 1 \left( \frac{6}{4} \right) = 1 \left( \frac{3}{2} \right) = \frac{3}{2} \]
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