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Question

Question 17
Which term of the AP 53, 48, 43,…. Is the first negative term?

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Solution

Given AP is 53, 48, 43, ……
First term (a) = 53 and common difference (d) = 48 – 53 = - 5
Let nth term of the AP be the first negative term.
i.e., Tn<0 [ nth term of an AP, Tn=a+(n1)d]
(a + (n - 1)d) < 0
53 + (n - 1)(-5) < 0
53 - 5n + 5 < 0
58 - 5n < 0 5n > 58
n > 11.6 n = 12
i.e., 12th term is the first negative term of the given AP.
T12 = a + (12 - 1)d = 53 + 11 (-5)
= 53 - 55 = -2 < 0

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