IIT JEE , AIEEE Forum - Mathematics , Algebra

nano0101

OK

_{^{Let the series be a,a+d,a+2d .................}}

when n=7

S_{7 ^{< 0}}

_{^{7/2 ( 2a+6d) < 0}}

_^a+3d<0

_{^{means the 4th term < 0}}

_{^{when n= 11}}

_^S11>0

_{11/2(2a+10d)>0}

_a+5d>0

_{the 6th term >0}

_{It means that till 4th term evry term must be -ve n after 6th term +ve . 5th cud be anything.}

_{thus a must be some -ve number.}

_{if 5th term is = 0}

_{then max no of terms = 10}

_{if 5th term>0}

_{max no of terms =9}

_{if 5th <0}

_{max no of term= 11}

_{since those 11 cud be anywhere in the series}

_{max no of terms = 12}

_{if it is more than that the fourth term will become more than 0}

_{thus answer =12}