Write the first five term of the sequence whose $n^{t h}$ term is $a_{n} = n \frac{n^{2} + 5}{4}$ .

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Solution

Substituting $n = 1, 2, 3, 4, 5$ , we obtain
$a_{2} = 1. \frac{1^{2} + 5}{4} = \frac{6}{4} = \frac{3}{2}$
$a_{2} = 2. \frac{2^{2} + 5}{4} = 2. \frac{9}{4} = \frac{9}{2}$
$a_{3} = 3. \frac{3^{2} + 5}{4} = 3. \frac{14}{4} = \frac{21}{2}$
$a_{4} = 4. \frac{4^{2} + 5}{4} = 21$
$a_{6} = 5. \frac{5^{2} + 5}{4} = 5. \frac{30}{4} = \frac{75}{2}$
Therefore, the required terms are $\frac{3}{2}, \frac{9}{2}, \frac{21}{2}, 21 a n d \frac{75}{2}$

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