Write the first five terms of the sequences whose nth term is a_n=n\dfrac{n^2+5}{4}

On substituting n = 1, 2, 3, 4, 5, we get first 5 terms

\(a_1=1. \dfrac{1^2+5}{4}\)

\( a_1=\dfrac{6}{4}=\dfrac{3}{2}\)

\( a_2=2. \dfrac{2^2+5}{4}\)

\( a_2=\dfrac{18}{4}=\dfrac{9}{2}\)

\( a_3=3. \dfrac{3^2+5}{4}\)

\( a_3= \dfrac{42}{4}=\dfrac{21}{2}\)

\( a_4=4. \dfrac{4^2+5}{4}\)

\( a_4=\dfrac{84}{4}=21\)

\( a_5=5. \dfrac{5^2+5}{4}\)

\( a_5= \dfrac{150}{4}=\dfrac{75}{2}\)

Hence, the required terms are \( \dfrac{3}{2}\), \( \dfrac{9}{2}\),\( \dfrac{21}{2}\) , 21 and \( \dfrac{75}{2}\).