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Question
Which term of the sequence 114, 109, 104, ... is the first negative term?
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Solution
Here, A.P is 114, 109, 104, ..
So, first term, a = 114
Now,
Common difference (d) = a1 - a
= 109 - 114
= -5
Now, we need to find the first negative term,
an < 0
114 + (n-1) (-5) < 0
114 - 5n + 5 < 0
119 - 5n < 0
5n > 119
Further simplifying, we get,
n > `119/5`
n > 23 `4/5`
n ≥ 24 (as n is a natural m=number)
Thus, n = 24
Therefore, the first negative term is the 24th term of the given A.P.
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