Answer :

Let first term be a and common difference be d.
We know that, an = a + (n - 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



a3 = a + (3 - 1)d
4 = a + 2d …(i)
and a9 = a + (9 - 1)d
-8 = a + 8d …(ii)


On solving eq. (i) and (ii), we get,
a = 8 and d = -2


Let the nth term be zero.
an = a + (n - 1)d
0 = 8 + (n - 1) × (-2)
0 = 8 – 2n -2(-1)
0 = 8 – 2n + 2
-10 = – 2n
n = 5


Hence, 5th will be zero.


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