The sequence a (n) is defined …
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Yogita Ingle 6 years, 2 months ago
Nth term of the sequence is given by t_n = (n - 1)(n -2 )(n -3 ), here n is integers e.g., n = 1, 2, 3, 4, .........
First term , put n = 1
Then, t₁ = (1 - 1)(1 - 2)(1 - 3) = 0 × (-1) × (-2) = 0
2nd term, put n = 2
Then, t₂ = (2 - 1)(2 - 2)(2 - 3) = 1 × 0 × (-1) = 0
3rd term , put n = 3
Then, t₃ = (3 - 1)( 3 - 2)(3 - 3) = 2 × 1 × 0 = 0
Here it is clear that first three terms of the sequence are zero.
Now, put n = 4
Then, t₄ = (4 - 1)(4 - 2)(4 - 3) = 3 × 2 × 1 = 6 > 0 e.g., positive
Put n = 5
Then, t₅ = (5 - 1)(5 - 2)(5 - 3) = 4 × 3 × 2 = 24 > 0 e.g., positive
Hence, after 3rd term all the terms of the sequence are positive.
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