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Question
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.
Solution
The given A.P. is 21, 18, 15, .......
Here, first term a = 21 and common difference d = 18 – 21 = 3
Let nth term of the given A.P. be –81
`=>` –81 = a + (n – 1)d
`=>` –81 = 21 + (n – 1) × (–3)
`=>` –102 = (n – 1) × (–3)
`=>` n – 1 = 34
`=>` n = 35
Thus, the 35th term of the given A.P. is –81.
Let pth term of this A.P. be 0
`=>` 21 + (p – 1) × (–3) = 0
`=>` 21 – 3p + 3 = 0
`=>` p = 8
Thus, 8th term of this A.P. is 0
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