Can you guess the other terms?

It is an arithmetic progression with $d=\dfrac{23}{2}-\dfrac{7}{2}=\dfrac{39}{2}-\dfrac{23}{2}=8$ . Use the formula $a_n=a_1+(n-1)d$ . The unkown terms terms are:

$x=a_1+4d=\dfrac{7}{2}+4(8)=\dfrac{71}{2}$

$y=a_1+6d=\dfrac{7}{2}+6(8)=\dfrac{103}{2}$

$z=a_1+8d=\dfrac{7}{2}+8(8)=\dfrac{135}{2}$

The desired answer is: $x+y+z=\dfrac{71}{2}+\dfrac{103}{2}+\dfrac{135}{2}=$ $\boxed{\dfrac{309}{2}}$