Correct Answer: 0

Solution : Given: 7 times the 7 ^th term of AP = 11 times its 11 ^th term
Formula for n ^th term $⇒a+(n-1)d$
where $a$ = 1 ^st term, $d$ = common difference and $n$ = number of terms
⇒ $7 × a_7 = 11 × a_{11}$
$⇒7[a+(7-1)d]=11[a+(11-1)d]$
$⇒7a+42d=11a+110d$
$⇒11a-7a+110d-42d=0$
$⇒4a+68d=0$
$⇒4(a+17d)=0$
$⇒a+17d=0$ ------------------------------(1)
Similarly, $a_{18}= [a +(18-1)d] = a+17d$
By using equation (1) we get,
⇒ $a_{18}= 0$
So, the 18 ^th term is 0.
Hence, the correct answer is 0.