Question

Which term of

a.p 163,160,167.....is the first negative term?

Answer 1

d = 160 - 163= -3
first negative term will be smaller than zero
so
0> a+ (n-1)d
0> 163 + (n-1)-3
-163 > -3n + 3
-166 > -3n
or
166 > 3n
$\frac{166}{3} > \: n \\ 55 \times \frac{1}{3 } > n$
hence
n= 56
therefore the 56th term is the first negative term

Answer 2

Refer to the attachment above :)