(v) Which term of the AP $121,117.113,$ … is its first negative term?
An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.
Solution:
(v) Given A.P is $121,117,113,$ ………..
Fiat term $\left( a \right)=121$
Common difference $\left( d \right)=117-121=-4$
We know that, ${{n}^{th}}$ term ${{a}_{n}}=a+\left( n-1 \right)d$
And, for some ${{n}^{th}}$ term is negative i.e., ${{a}_{n}}<0$
$121+\left( n-1 \right)-4<0$
$121+4-4n<0$
$125-4n<0$
$4n>125$
$n>125/4$
$n>31.25$
The integer which comes after $31.25$ is $32.$
$\therefore {{32}^{nd}}$ term in the A.P will be the first negative term.