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A sequence whose nth term is given by a(...

A sequence whose nth term is given by `a_(n) = 2n^(2) + pn - 3p^(2)` is such that `a_(3) = 0`. Determine the sequence explicitly and then show that `a_(n) gt 0` for all `n ge 4`.

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The correct Answer is:
`a_(n) -2n^(2) - 2n - 12 (AA n in NN)` or, `a_(n) = 2n^(2) - 3n - 27`
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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 A (Very short Answer Type Questions)
  1. Write the first five terms of the sequence defined by u(n) = (n)+(n...

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  2. Write the first five terms of the sequence defined by u(n) = (-1)^(...

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  3. Write the first five terms of the sequence defined by u(n) = 2n^(2)...

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  4. Find the 6th and rth terms of the sequence {1, 8, 27, 64,..}.

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  5. Prepare a series to first n terms of the sequence {(1)/(5),(1)/(7), (1...

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  6. Find the 11th term of the sequence {(1)/(2), (1)/(3), (1)/(5), (1)/(8)...

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  7. Find the 25th and 50th terms of the sequence whose nth terms is given ...

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  8. Write the series Sigma(r=1)^(n) (r^(2)+1)/(2r^(2) - 1) in expanded for...

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  9. Determine the first five terms of the sequence defined by, u(1) = -2, ...

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  10. Write the series (3)/(2)+1 + (7)/(10) + (9)/(17) +…+(2r+1)/(r^(2) + 1)...

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  11. Determine the first five terms of the sequence defined by, u(1) = 4 an...

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  12. Write the series Sigma(r=1)^(n) (2r+1)/(r^(2) + 1) in expanded form.

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  13. If S(n) = u(1) +u(2) + ….+ u(n) = n^(2) + 2n, find the first four term...

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  14. If the rth term of the sequence {u(n)} is u(r) = (-1)^(r-1). 3^(2-r), ...

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  15. The sum of first r terms of a series is ar^(2) + br, find the first an...

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  16. For the sequence {u(n)} if u(1) - 2 and u(r+1) = u(r) +r+2, for all na...

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  17. For the sequence {u(n)} if u(1) = (1)/(4) and u(n+1) = (u(n))/(2+u(n))...

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  18. Find the least value of n, for which the nth term a(n) of the sequence...

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  19. A sequence whose nth term is given by a(n) = 2n^(2) + pn - 3p^(2) is s...

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