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Q.

Which term of the AP 20,19 1 4 ,18 1 2 ,17 3 4 , is its first negative term?


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a

25th

b

20th

c

30th 

d

28th

answer is C.

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Detailed Solution

Given A.P. 20,19 1 4 ,18 1 2 ,17 3 4
So, first term: t 1  = 20 .
Second term:
t 2 =19 1 4 t 2 = 77 4 d = t 2 t 1 d = 77 4 20 = 3 4
Let n th  terms of A.P be first negative term:    Therefore,  t n <0 .  Formula used for n th term of A.P.:  t n =a+ n1 d Applying the formula of n th  terms of A.P:    20+(n1) 3 4 <0 20 3n 4 + 3 4 <0 803n+3<0 833n<0 83<3n n> 83 3 n>27 2 3 n28
Therefore, 28th term is the first negative term of A.P.
Hence, option (3) is correct.
 
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