What is the next number in this sequence: $\dfrac12, 2, 5, 11, 23, 47, 95, \ldots$?

$$\small{\text{
What is the next number in this sequence: $\dfrac12, 2, 5, 11, 23, 47, 95, \ldots$?
}}$$

$$\small{\text{$
t_1 = \dfrac{1}{2}
$}}\\\\
\small{\text{$
\begin{array}{rcl}
t_n &=& 2^{n-1}t_1 +\sum \limits_{k=0}^{n-2}2^k \qquad | \qquad \sum \limits_{k=0}^{n-2}2^k = 2^{n-1}-1 \\\\
t_n &=& 2^{n-1}t_1 + 2^{n-1}-1 \\\\
t_n &=& 2^{n-1}(1+t_1)-1 \\\\
t_n &=& 2^{n-1}\left(1+\dfrac{1}{2}\right)-1 \\\\
t_n &=& 2^{n-1}\left(\dfrac{3}{2}\right)-1 \\\\
\mathbf{t_n} & \mathbf{=} & \mathbf{3\cdot 2^{n-2}-1} \\\\
t_8 &=& 3\cdot 2^6-1\\\\
t_8 &=& 3\cdot 64 - 1 \\\\
\mathbf{t_8} & \mathbf{=} & \mathbf{191}
\end{array}
$}}$$

1/2 , 2, 5, 11, 23, 47, 95

The next term is found by doubling the previous term and adding 1  =   2(95) + 1   = 191