Question

Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are: an = n n2 + \(\frac{5}{4}\).

Answer 1

Substituting n = 1, 2, 3, 4, 5, we obtain

a1 = 1.12+\(\frac{5}{4}=\frac{6}{4}=\frac{3}{2}\)

a2 = 2.22+\(\frac{5}{4}=\frac{2.9}{4}=\frac{9}{2}\)

a3 = 3.32+\(\frac{5}{4}=\frac{3.14}{4}=\frac{21}{2}\)

a4 = 4.42+\(\frac{5}{4}\) = 21

a5 = 5.52+\(\frac{5}{4}=\frac{5.30}{4}=\frac{75}{2}\)

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