If the third and the ninth terms of an AP are 4 and –8 respectively, which term of this AP is zero?

If the third and the ninth terms of an AP are 4 and –8 respectively,

1.	If the third and the ninth terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Answer» given 3rd term = 4i.e, a+2d=4 ---- 1and 9th term = -8i.e., a+8d=-8 ------------- 2by by subtacting 1 and 2 we get, a+2d = 4 a+8d = -8 - - + ---------------- -6d = 12 ---------------so, d = -12/6 d = -2substitute it in (1) we get,\xa0a+2(-2) = 4a = 4+4 =8a=8\ufeff\ufeffhere we get a=82nd term = a+d = 8+(-2) = 8-2 = 63d term = a+2d = 8+2(-2) = 8-4 = 44th term = a+3d = 8+2(-3) = 8-6 = 25th term = a+4d = 8+2(-4) = 8-8 =06th 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 placeso, 5th number in the series is 0.\xa0