Mathematics
If the third and the 9th terms of an A.P. be 4 and -8 respectively, find which term is zero?
AP
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Answer
Let the first term be a and common difference be d of the A.P.
Given,
⇒ a3 = a + (3 - 1)d
⇒ a + 2d = 4 ……..(i)
⇒ a9 = a + (9 - 1)d
⇒ a + 8d = -8 ……..(ii)
Subtracting (i) from (ii) we get,
⇒ a + 8d - (a + 2d) = -8 - 4
⇒ 8d - 2d = -12
⇒ 6d = -12
⇒ d = -2.
Substituting value of d in (i) we get,
⇒ a + 2(-2) = 4
⇒ a - 4 = 4
⇒ a = 8.
Let nth term be zero.
⇒ an = 0
⇒ a + (n - 1)d = 0
⇒ 8 + (n - 1)(-2) = 0
⇒ 8 - 2n + 2 = 0
⇒ 2n = 10
⇒ n = 5.
Hence, 5th term = 0.
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