Question

Which term of the $A.P$ $25,20,\mathrm{15.......}$ is the first $-ve$ term.

Answer 1

Given,

$a=25$

$d=20-25=-5$

$T_n<0$

$a+(n-1)d<0$

$25+(n-1)(-5)<0$

$25<5(n-1)$

$5<(n-1)$

$n>6$

$\Rightarrow n=7$

7th term is negative.

$a_7=25+(7-1)(-5)$

$=25-5\times 6$

$=-5$