The sum of the first nine terms of an arithmetic progression is 171. Which one of the following statements is not correct about this A.P.?

Let a be the first term of A.P and d be the common difference.

$\therefore$ Sum of n term of an AP = ${\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2\mathrm{a}+(\mathrm{n}-1)\cdot \mathrm{d}]$

where n  be the number of terms =9 (given)

$171=\frac{9}{2}[2a+(9-1\left)d\right]$

$38=2a+8d=a+(a+8d)=$ first term +ninth term

From this we conclude that no term of the A.P. can be determined. But the statement that sum of first and ninth term can't be determined is not correct.