Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 35

The common difference is: $d=-2.$ The initial term: $a_1=28.$ $a_n=30-2n$, $a_n=a_{n-1}-2$

We know that $a_{15}=0,a_{40}=-50$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{40}-a_{15}}{40-15}=\frac{-50-0}{25}=-2.$ The initial term: $a_1=a_n-(n-1)d=a_{15}-(14)(-2)=0-(14)(-2)=28.$ Thus: $a_n=a_1+(n-1)d=28+(n-1)(-2)=30-2n$, $a_n=a_{n-1}+d=a_{n-1}-2$