Answer
$d=-2.7$
$a_{n}=17.7-2.7n $
$ a_{5}=4.2;$
$a_{100}=-252.3$
Work Step by Step
$d=a_{n+1}-a_{n}=12.3-15=9.6-12.3=6.9-9.6=-2.7$
$a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=15$
$a_{n}=a+\left( n-1\right) d=15+\left( n-1\right) \times \left( -2.7\right) =15-2.7n+2.7=17.7-2.7n$
$a_{n}=17.7-2.7n\Rightarrow a_{5}=17.7-2.7\times 5=4.2;a_{100}=17.7-2.7\times 100=-252.3$
