Given first term a1 = 1 and the recursive formula is given:
[tex]a_n=\frac{a_{n-1}}{2}-1[/tex]
We have to find the next four terms of the sequence.
The second term is:
[tex]\begin{gathered} a_2=\frac{a_{2-1}}{2}-1_{} \\ =\frac{1}{2}-1 \\ =-\frac{1}{2} \end{gathered}[/tex]
The third term is :
[tex]\begin{gathered} a_3=\frac{a_{3-1}}{2}-1 \\ =\frac{a_2}{2}-1 \\ =\frac{\frac{-1}{2}}{2}-1 \\ =-\frac{1}{4}-1 \\ =-\frac{5}{4} \end{gathered}[/tex]
The fourth term is:
[tex]\begin{gathered} a_4=\frac{a_{4-1}}{2}-1 \\ =\frac{a_3}{2}-1 \\ =\frac{\frac{-5}{4}}{2}-1 \\ =-\frac{5}{8}-1 \\ =-\frac{13}{8} \end{gathered}[/tex]
The fifth term is:
[tex]\begin{gathered} a_5=\frac{a_{5-1}}{2}-1 \\ =\frac{\frac{-13}{8}}{2}-1 \\ =-\frac{13}{16}-1 \\ =-\frac{29}{16} \end{gathered}[/tex]
Thus, option D is correct.
