Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - 12.1 Exercises - Skill Practice - Page 798: 24

n-th term:$\quad a_{n}=5.8-1.6n$, The next term is $\quad a_{6}=-3.8$

$4.2-1.6=2.6$ $2.6-1.6=1$ $1-1.6=0.6...$ We can write 4.2 as $5.8-1.6.$ $n=1,\quad 4.2=5.8-1.6$ $n=2,\quad 2.6=4.2-1.6\quad =5.8-2\times(1.6)$ $n=3,\quad 1=2.6-1.6=5.8-3\times(1.6)$ $n=4,\quad -0.6=1-1.6=5.8-4\times(1.6)\quad...$ So, the nth term is $a_{n}=5.8-1.6n$, and the next term is $a_{6}=-2.2-1.6=-3.8$ (also, $5.8-6(1.6)=5.8-9.6=-3.8$)