Question

Which term of the $AP:121,117,113,...,$ is its first negative term?

[Hint : Find n for $a_{nm}<0$]

Answer 1

Given the AP series is $121,117,113,....$
Thus, first term, $a=121$
Common difference, $d=117-121=-4$
By the nth term formula,
$a_n=a+(n-1)d$
Therefore,
$a_n=121+(n-1)(-4)$
$=121-4n+4$
$=125-4n$
To find the first negative term of the series, $a_n<0$
Therefore,
$125-4n<0$
$125<4n$
$n>125/4$
$n>31.25$
Therefore, 32nd term will be the first negetive term.