Mathematics
Which term of the series :
21, 18, 15, …….. is -81 ?
Can any term of this series be zero ?
If yes, find the number of terms.
AP
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Answer
In A.P. 21, 18, 15, ……..,
d = 18 - 21 = -3 and a = 21.
Let nth term be -81.
⇒ an = -81
⇒ a + (n - 1)d = -81
⇒ 21 + (n - 1)(-3) = -81
⇒ 21 - 3n + 3 = -81
⇒ 24 - 3n = -81
⇒ 3n = 24 + 81
⇒ 3n = 105
⇒ n = 35.
Let rth term be 0.
⇒ ar = 0
⇒ a + (r - 1)d = 0
⇒ 21 + (r - 1)(-3) = 0
⇒ 21 - 3r + 3 = 0
⇒ 24 - 3r = 0
⇒ 3r = 24
⇒ r = 8.
Hence, -81 is 35th and 0 is 8th term of an A.P.
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