Question

If the 3rd and the 9th terms of an AP are 4 and -8 respectively,which term of this AP is Zero?

Answer 1

formula is last term =first term -(n-1)difference
4=a+(2)d                                       equation 1
-8=a+8d                                        equation 2
 by solving both we get d=-2
then by substituting that in any of the equation we get the first term as 8
therefore the term which is 0 is 5th term   

Answer 2

given 3rd term = 4
i.e, a+2d=4 ---- 1
and 9th term = -8
i.e., a+8d=-8 ------------- 2
by by subtacting 1 and 2 we get,
      a+2d = 4
      a+8d = -8
     -    -      +
     ----------------
        -6d = 12
     ---------------
so, d = -12/6
      d = -2
substitute it in (1) we get, 
a+2(-2) = 4
a = 4+4 =8
a=8

here we get a=8

2nd term = a+d = 8+(-2) = 8-2 = 6
3d term = a+2d = 8+2(-2) = 8-4 = 4
4th term = a+3d = 8+2(-3) = 8-6 = 2
5th term = a+4d = 8+2(-4) = 8-8 =0
6th term = a+5d =8+5(-2) = 8-10 = -2 .......

so the series we got is 8,6,4,2,0,-2.....
here we get zero at 5th place
so, 5th number in the series is 0