Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises - Page 704: 10

$6,6,3,1,\frac{1}{4},...$

Given: $a_{1}=6,a_{(n+1)}=\frac{a_{n}}{n}$ $a_{1}=6$ $a_{1+1}=a_{(2)}=\frac{a_{1}}{1}=\frac{6}{1}=6$ $a_{2+1}=a_{(3)}=\frac{a_{2}}{2}=\frac{6}{2}=3$ $a_{3+1}=a_{(4)}=\frac{a_{3}}{3}=\frac{3}{3}=1$ $a_{4+1}=a_{(5)}=\frac{a_{4}}{4}=\frac{1}{4}=\frac{1}{4}$ Hence we see that the first five terms are $6,6,3,1,\frac{1}{4}$