An arithmetic progression

We just have to insert its arithmetic mean. So, the answer is $\left(\dfrac{3}{8} + \dfrac{41}{24}\right) ÷ 2= \dfrac{25}{24}$
So, $a + b = \color{#69047E}{\boxed{49}}$ .

Alternate solution:

$a=\dfrac{3}{8} \implies$ Eq.(1)

$a+2d = \dfrac{41}{24} \implies$ Eq.(2)

Substitute Eq.(1) into Eq. (2):

$\dfrac{3}{8} + 2d = \dfrac{41}{24}\\ 2d=\dfrac{41-9}{24}\\ d=\dfrac{32}{24(2)} = \dfrac{16}{24}$

$x=a+d=\dfrac{3}{8} + \dfrac{16}{24} = \dfrac{9+16}{24} = \dfrac{25}{24}$

$a=25,b=24$ and $a+b=25+24=\boxed{49}$