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Which term of the AP $20, 1914, 1812, 1734, …$ is its first negative term?

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25th

20th

30th

28th

answer is C.

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Detailed Solution

Given A.P.

20, 1914, 1812, 1734 … …

So, first term:

t 1 = 20

.
Second term:

t 2 = 1914 ⇒ t 2 = 774

∴ d = t 2 − t 1 ⇒ d = 774 − 20 = − 3 4

Let

n t h terms of A .P be first negative term:

Therefore, t n < 0

. Formula used for

n t h

term of A.P.:

t n = a + n − 1 d

Applying the formula of

n t h terms of A .P:

∴ 20 + (n − 1) − 3 4 < 0 ⇒ 20 − 3 n 4 + 34 < 0 ⇒ 80 − 3 n + 3 < 0 ⇒ 83 − 3 n < 0

⇒ 83 < 3 n ⇒ n > 833 ⇒ n > 2723 ∴ n ≃ 28

Therefore, 28th term is the first negative term of A.P.
Hence, option (3) is correct.

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