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Show that the sequence $space space open curly brackets straight t subscript straight n close curly brackets$ defined by $straight t subscript straight n space equals space 2 straight n squared plus straight n plus 1$ is not an A.P.

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12.
Which term of an A.P. 5, 2, -1, ......... is -22?

The given A.P. is: 5, 2, - 1,...............

Here a = 5, d = 2 - 5 = -3

Let -22 be the nth term

∴                         $straight t subscript straight n space equals space minus 22$                 or             a + (n - 1)d = -22

or             5 + (n - 1) (-3) = -22             or               5 - 3n + 3 = -22

or                    8 - 3n = -22                   or                       3n = 8 + 22

or                         3n = 30                    or                           n = 10

∴ -22 is the 10th term.

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13.

Which term of the sequence 12 + 8i, 11 + 6i, 10+41i, ....... is

(i) purely real (ii) purely imaginary?

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14.

Which term of the sequence $space space 24 comma space 23 1 fourth comma space 22 1 half comma space 21 3 over 4 comma space space.....$ is the first negative term?