Question:
Which term of the sequence 114, 109, 104, ... is the first negative term?
Solution:
Here, A.P is
So, first term,
Now,
Common difference (d) =
$=109-114$
$=-5$
Now, we need to find the first negative term,
$a_{n}<0$
$114+(n-1)(-5)<0$
$114-5 n+5<0$
$119-5 n<0$
$5 n>119$
Further simplifying, we get,
$n>\frac{119}{5}$
$n>23 \frac{4}{5}$
$n \geq 24$ (as $n$ is a natural number)
Thus, $n=24$
Therefore, the first negative term is the $24^{\text {* term }}$ of the given A.P.