Question
Which term of the sequence $114, 109, 104, ....$ is the first negative term?
✓
Answer
Here,
A.P. is $114, 109, 104, .....$
So, first term $a = 114$
Now,
Common difference $(d) = a_1 - a$
$= 109 - 114$
$= -5$
Now, we need to find the first negative term,
$a_n < 0$
$114 + (n - 1)(-5) < 0$
$114 - 5n + 5 < 0$
$119 - 5n < 0$
$5n > 119$
Further simplifying, we get,
$\text{n}>\frac{119}{5}$
$\text{n}>23\frac{4}{5}$
$\text{n}\geq24$ (as n is a natural number)
Thus, n = 24
Therefore, the first negative term is the $24^{th}$ term of the given A.P.
A.P. is $114, 109, 104, .....$
So, first term $a = 114$
Now,
Common difference $(d) = a_1 - a$
$= 109 - 114$
$= -5$
Now, we need to find the first negative term,
$a_n < 0$
$114 + (n - 1)(-5) < 0$
$114 - 5n + 5 < 0$
$119 - 5n < 0$
$5n > 119$
Further simplifying, we get,
$\text{n}>\frac{119}{5}$
$\text{n}>23\frac{4}{5}$
$\text{n}\geq24$ (as n is a natural number)
Thus, n = 24
Therefore, the first negative term is the $24^{th}$ term of the given A.P.
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