Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 37

The common difference is: $d=-2.$ The initial term: $a_1=25.$ $a_n=27-2n$, $a_n=a_{n-1}-2$

We know that $a_{14}=-1,a_{18}=-9$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{18}-a_{14}}{18-14}=\frac{-9-(-1)}{4}=-2.$ The initial term: $a_1=a_n-(n-1)d=a_{14}-(13)(-2)=-1-(13)(-2)=25.$ Thus: $a_n=a_1+(n-1)d=25+(n-1)(-2)=27-2n$, $a_n=a_{n-1}+d=a_{n-1}-2$