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Question
Which term of the A.P. 121, 117, 113 … is its first negative term?
[Hint: Find n for an < 0]
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Solution
Given A.P. is 121, 117, 113 …
a = 121
d = 117 − 121
d = −4
an = a + (n − 1) d
= 121 + (n − 1) (−4)
= 121 − 4n + 4
= 125 − 4n
We have to find the first negative term of this A.P.
Therefore, an < 0
125 - 4n < 0
125 < 4n
`n > 125/4`
n > 31.25
Therefore, 32nd term will be the first negative term of this A.P.
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