Answer: The correct option is B. The third term is 4.
Explanation:
The given recursive formula is,
[tex]a_n=\frac{2+a_{n-1}}{2}[/tex]
It is given that the first term is 10. So,
[tex]a_1=10[/tex]
To find third term, first we have to find the second term.
[tex]a_2=\frac{2+a_{2-1}}{2}[/tex]
[tex]a_2=\frac{2+a_{1}}{2}[/tex]
[tex]a_2=\frac{2+10}{2}[/tex]
[tex]a_2=\frac{12}{2}[/tex]
[tex]a_2=6[/tex]
Therefore the second term is 6.
[tex]a_3=\frac{2+a_{3-1}}{2}[/tex]
[tex]a_3=\frac{2+a_{2}}{2}[/tex]
[tex]a_3=\frac{2+6}{2}[/tex]
[tex]a_3=\frac{8}{2}[/tex]
[tex]a_3=4[/tex]
Therefore, the correct option is B. The third term is 4.
