k k k k k k kk kk

It is obvious that the polynomial $x^{4}-10x^{3}+35x^{2}-48x+23$ satisfies the values given for the integers from $1$ to $4$ . Hence, the next number must be $33$ when $x = 5$ . This question is invalid.

the pattern is= $2n-1$

$1+1^2+1^3=3,3+1^4+1^5=5,5+1^6+1^7,7+1^8+1^9=\boxed{9}$

The sequence is from the positive odd numbers.

The answer is the next odd number $\color{#69047E}{\boxed{9}}$ .

It's simple an A.P. of d=2

constant difference is 2 , 7+2=9

going up by 2's