According to the given problem,
[tex]\begin{gathered} a_1=9 \\ a_n=2\cdot a_{n-1}-1 \end{gathered}[/tex]
Obtain the second term as,
[tex]\begin{gathered} a_2=2\cdot a_1-1 \\ a_2=2\cdot(9)-1 \\ a_2=18-1 \\ a_2=17 \end{gathered}[/tex]
Similarly, the value of further terms can be calculated.
Obtain the third term as,
[tex]\begin{gathered} a_3=2\cdot a_2-1 \\ a_3=2\cdot(17)-1 \\ a_3=34-1 \\ a_3=33 \end{gathered}[/tex]
Obtain the fourth term as,
[tex]\begin{gathered} a_4=2\cdot a_3-1 \\ a_4=2\cdot(33)-1 \\ a_4=66-1 \\ a_4=65 \end{gathered}[/tex]
Obtain the fifth term as,
[tex]\begin{gathered} a_5=2\cdot a_4-1 \\ a_5=2\cdot(65)-1 \\ a_5=130-1 \\ a_5=129 \end{gathered}[/tex]
Thus, the first five terms of the sequence are 9, 17, 33, 65, 129.
Therefore, option (a) is the correct choice.
