Question

Which term of AP 121, 117,113................... is ther first negative terms.

Answer 1

Given terms of AP

$121,117,113,$….

First term $\left(a\right)=121$

Common difference $\left(d\right)=117-121=-4$

$\left(a_n\right)n^{th}$ term of AP$=a+(n-1)d$

$=121+(n-1)(-4)$

$=121-4n+4$

$=125-4n$

$a_n<0$

$\Rightarrow 125-4n<0$

$n>\frac{125}{4}$

$n>31.25$

$\therefore n\ge 32$

$n\Rightarrow$ Natural number

$32$ term is first negative term.