Question

Which term of the sequence $48,43,38,33$ is the first $-ve$ term?

Answer 1

As difference between subsequent terms in constant, $43-48=-5=$ common difference (d)

$\Rightarrow$ This sequence is an A.P. with $a=48,d=-5$

$n^{th}$ term, $a_n=a+(n-1)d<0$

$\Rightarrow 48+(n-1)(-5)<0$

$\Rightarrow 48-5n+5<0$

$\Rightarrow 53<5n\Rightarrow n>\frac{53}{5}$

$\Rightarrow n>10.6$

As $n\in Z$

$\Rightarrow n=11$.