Answer:
The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].
Step-by-step explanation:
We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:
{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}
From the given options, we can put in the values of n and check if it proves to be true.
For [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.
[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]
[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]
[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]
[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]
[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]
Therefore, the formula for the given sequence is [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].
Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]
