Answer:
The sequence is given below as
[tex]8,11,14,17,20[/tex]
Step 1:
The nth term of an arithmentic progression is given below as
[tex]\begin{gathered} a_n=a+(n-1)d \\ where, \\ a=first\text{ term} \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}[/tex]
To figure out the common difference, we will use the formula below
[tex]\begin{gathered} d=a_2-a_1=a_3-a_2 \\ d=11-8=14-11=17-14=20-17=3 \\ d=3 \end{gathered}[/tex]
Step 2:
The first term of the sequence is given below as
[tex]a=8[/tex]
Step 3:
Substitute the value of a and d in the formula below
[tex]\begin{gathered} a_{n}=a+(n-1)d \\ a_n=8+(n-1)3 \\ a_n=8+3n-3 \\ a_n=5+3n \end{gathered}[/tex]
Hence,
The final answer is
[tex]a_n=5+3n,where\text{ n=1,2,3,4,...}[/tex]
OPTION A is the right answer
