Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 45

$a_1=A \\ a_2=a_1+ d=A+d\\ a_3=a_2+d =(A+d)+d =A+2d \\ a_4=a_3+d =(A+2d)+d =A+3d \\ a_5=a_4+d =(A+3d)+d =A+4d $

We are given that $a_n=a_{n-1}+ d$ and $a_1=A$. In order to determine the remaining values, we will have to substitute $n=3,4,5$ into the given sequence. We use previous terms to compute successive terms as follows: $ a_2=a_1+ d=A+d\\ a_3=a_2+d =(A+d)+d =A+2d \\ a_4=a_3+d =(A+2d)+d =A+3d \\ a_5=a_4+d =(A+3d)+d =A+4d $