Chapter 11 - 11.2 - Arithmetic Sequences and Partial Sums - 11.2 Exercises - Page 786: 14

$a_1=97$ $a_2=94$ $a_3=91$ $a_4=88$ $a_5=85$ It is an arithmetic sequence. $d=-3$

$a_n=100-3n$ $a_1=100-3(1)=100-3=97$ $a_2=100-3(2)=100-6=94$ $a_3=100-3(3)=100-9=91$ $a_4=100-3(4)=100-12=88$ $a_5=100-3(5)=100-15=85$ A sequence is arithmetic if $a_2−a_1=a_3−a_2=a_4−a_3=a_5−a_4=...=d$ For the given sequence we have that: $a_2-a_1=94-97=-3$ $a_3-a_2=91-94=-3$ $a_4-a_3=88-91=-3$ $a_5-a_4=85-88=-3$ It is an arithmetic sequence. Common difference: $d=-3$