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Among the subsequent terms, which term of an AP 25, 20, 15,... is the first negative term?

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answer is B.

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Detailed Solution

It is given that an AP is 25, 20, 15, ….
We have to find the term which has the first negative term.
From the given arithmetic progression

a = 25

and,

d = 20 − 25 d = − 5

Assume that the nth term of the given AP is the first negative term.
Since we have to find the negative term, the nth term will be less than zero.
Then,

a n < 0

.
So, since

a n = a + (n − 1) d

a + (n − 1) d < 0

Substitute the known values,

25 + (n − 1) (− 5) < 0 − 5 (n − 1) < − 25 n − 1 > 5 n > 6

Since, for n > 6, all the terms have negative value.
So the first negative term will appear in the 7th term.
The correct answer is option 2).

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