Answer:
a) [tex]a_n=3n-2[/tex]
b) [tex]a_n=a_{n-1}+3[/tex]
c) [tex]a_{15}=43[/tex]
Step-by-step explanation:
Arithmetic Sequences
In an arithmetic sequence, each number is obtained as the previous number plus or minus a constant value known as the common difference. The general term for an arithmetic sequence is
[tex]a_n=a_1+(n-1)r\ ,\ n\geq 1[/tex]
where a_1 is the first term, r the common difference and n the number of terms
If we wanted to express the sequence in the recursive form, we only need to write each term as a function of the previous term.
[tex]a_n=a_{n-1}+r[/tex]
a) We can see in the graph the following sequence: 1, 4, 7 where clearly each term equals the previous term plus 3 (the common difference). So our general term is
[tex]a_n=1+3(n-1)[/tex]
[tex]a_n=1+3n-3[/tex]
[tex]a_n=3n-2[/tex]
b) The recursive expression is
[tex]a_n=a_{n-1}+3[/tex]
c) To determine [tex]a_{15}[/tex], we use n=15 in the general term
[tex]a{15}=3(15)-2=45-2[/tex]
[tex]a_{15}=43[/tex]
