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Question
Which term of the AP `20, 19 1/4 , 18 1/2 , 17 3/4 ` ,..... is the first negative term?
Solution
The given AP is `20, 19 1/4 , 18 1/2 , 17 3/4 ` ,.....
`Here, a = 20 and d = 19 1/4 -20 = 77/4 - 20 = (77-80)/4 = -3/4`
Let the nth term of the given AP be the first negative term. Then,
an < 0
`⇒ 20+ (n-1) xx (-3/4) < 0 [ a_n = a + (n-1) d]`
`⇒ 20+ 3/4 - 3/4 n<0`
`⇒ 83/4 - 3/4 n< 0 `
`⇒-3/4 n < - 83/4`
`⇒ n > 83/3 = 27 2/3`
∴ n= 28
Hence, the 28th term is the first negative term of the given AP.
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