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Question
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(- 1)^"n"/"n"`
Solution
Given the nth term an = `(- 1)^"n"/"n"`
a1 = `(- 1)^2/1` = – 1
a2 = `(- 1)^2/2 = 1/2`
a3 = `(- 1)^3/3 = -1/3`
a4 = `(- 1)^4/2 = 1/4`
a5 = `(- 1)^5/2 = - 1/5`
a6 = `(- 1)^6/6 = 1/6`
∴ The given sequence is `- 1, 1/2, - 1/3, 1/4, - 1/5, 1/6`.
This sequence is neither A.P, .P nr AGP.
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