Answer :
Answer: 17 , 23 , 29 , 35 and 41
Step-by-step explanation:
Given : [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 6 , where n≥1 , it means n can pick values from 1 and above
[tex]\\[/tex]When n = 1 , the sequence becomes
[tex]a_{1+1}[/tex] = [tex]a_{1}[/tex] + 6
[tex]\\[/tex]And it has been given that [tex]a_{1}[/tex] = 11 , substitute this value into the sequence, that is
[tex]\\[/tex][tex]a_{2}[/tex] = 11 + 6
[tex]\\[/tex][tex]a_{2}[/tex] = 17
[tex]\\[/tex]Also , when n = 2 , the sequence becomes
[tex]\\[/tex][tex]a_{3}[/tex] = [tex]a_{2}[/tex] + 6
[tex]\\[/tex]substituting the value of [tex]a_{2}[/tex] , we have
[tex]\\[/tex][tex]a_{3}[/tex] = 17 + 6 = 23
[tex]\\[/tex]When n = 3 , the sequence becomes
[tex]\\[/tex][tex]a_{4}[/tex] = [tex]a_{3}[/tex] + 6
[tex]\\[/tex]substituting the value of [tex]a_{3}[/tex], we have
[tex]\\[/tex][tex]a_{4}[/tex] = 23 + 6 = 29
[tex]\\[/tex]When n = 4 , the sequence becomes
[[tex]\\[/tex][tex]a_{5}[/tex] = [tex]a_{4}[/tex] + 6 , substituting the value of [tex]a_{4}[/tex] , we have
[tex]\\[/tex][tex]a_{5}[/tex] = 29 + 6 = 35
[tex]\\[/tex]And finally , when n = 5 , the sequence becomes
[tex]\\[/tex][tex]a_{6}[/tex] = [tex]a_{5}[/tex] + 6
[tex]\\[/tex]Substituting the value of [tex]a_{5}[/tex] , we have
[tex]\\[/tex][tex]a_{6}[/tex] = 35 + 6 = 41
[tex]\\[/tex]Therefore , the first five terms are : 17 , 23 , 29 ,35 and 41