Solution

In this series, the $n^\text{th}$ term can be found by the formula $2^{n-1}+1$ .

$\implies 7^\text{th}$ term $= 2^{7-1}+1=2^6+1=64+1=\boxed{65}$

Easier way to see this

Each next term is adding a next power of two.

$2+1=3$

$3+2=5$

$5+4=9$

$9+8=17$

$17+16=33$

$33+32=\boxed{65}$

An easier method to solve this is as follows:

The difference between any 2 consecutive number gets multiplied after every number , or

say, the difference between 2 & 3 is 1

the difference between 3 &5 is 2

so you see they are getting doubled , so

the difference between 17 & 33 is 16 so(33 +(16*2 =))65

$2 \quad \underrightarrow{{\color{#3D99F6}{+2^{0}}}} \quad 3 \quad \underrightarrow{{\color{#3D99F6}{+2^{1}}}} \quad 5 \quad \underrightarrow{{\color{#3D99F6}{+2^{2}}}} \quad 9 \quad \underrightarrow{{\color{#3D99F6}{+2^{3}}}} \quad 17 \quad \underrightarrow{{\color{#3D99F6}{+2^{4}}}} \quad 33 \quad \underrightarrow{{\color{#3D99F6}{+2^{5}}}} \quad {\color{#D61F06}{\boxed{65}}}$