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Question
Which term of the AP: 53, 48, 43,... is the first negative term?
Solution
Given AP is 53, 48, 43,...
Whose 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 + (n – 1)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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