Question

Write the first five terms of the sequences whose $n^{th}$ term is :

$a_n=n\frac{n^2+5}{4}$

Answer 1

$a_n=n\frac{n^2+5}{4}$.

Putting n = 1, 2, 3, 4 and 5, we have

$a_1=1.\frac{1^2+5}{4}=1.\frac{1+5}{4}=\frac{6}{4}=\frac{3}{2}$

$a_2=2.\frac{2^2+5}{4}=2.\frac{4+5}{4}=\frac{18}{4}=\frac{9}{2}$

$a_3=1.\frac{3^2+5}{4}=3.\frac{9+5}{4}=3.\frac{14}{4}=\frac{42}{4}=\frac{21}{2}$

$a_4=4.\frac{4^2+5}{4}=4.\frac{16+5}{4}=\frac{84}{4}=21$

$a_5=5.\frac{5^2+5}{4}=5.\frac{25+5}{4}=\frac{5\times 30}{4}=\frac{150}{4}=\frac{75}{2}$

Thus, the first five terms of the sequences are :

$\frac{3}{2},\frac{9}{2},\frac{21}{2},21,\text{and}\frac{75}{2}.$