Answer:
a) [tex]a_n=3n-1[/tex]
b) [tex]a_n=2n+7[/tex]
Step-by-step explanation:
a) From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:
14 - 11 = 3
11 - 8 = 3
8 - 5 = 3
5 - 2 = 3
(so the common difference = 3)
General equation of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
(where [tex]a[/tex] is the first term and [tex]d[/tex] is the common difference between terms)
Given:
[tex]\implies a_n=2+(n-1)3[/tex]
[tex]\implies a_n=2+3n-3[/tex]
[tex]\implies a_n=3n-1[/tex]
b) From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:
17 - 15 = 2
15 - 13 = 2
13 - 11 = 2
11 - 9 = 2
(so the common difference = 2)
General equation of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
(where [tex]a[/tex] is the first term and [tex]d[/tex] is the common difference between terms)
Given:
[tex]\implies a_n=9+(n-1)2[/tex]
[tex]\implies a_n=9+2n-2[/tex]
[tex]\implies a_n=2n+7[/tex]
