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11.
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.

Here, $straight t subscript straight n space equals space 2 straight n squared plus straight n plus 1$

Replacing by n - 1, we get

 $straight t subscript straight n minus 1 end subscript space equals space 2 left parenthesis straight n minus 1 right parenthesis squared plus left parenthesis straight n minus 1 right parenthesis space plus 1 space equals space 2 left parenthesis straight n squared space minus space 2 straight n space plus space 1 right parenthesis space plus space straight n minus 1 space plus 1$

 $equals 2 straight n squared minus 4 straight n plus 2 plus straight n space equals space 2 straight n squared minus 3 straight n plus 2$ $equals 2 straight n squared minus 4 straight n plus 2 plus straight n space equals space 2 straight n squared minus 3 straight n plus 2$

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 $equals 2 straight n squared plus straight n plus 1 minus 2 straight n squared plus 3 straight n minus 2 space equals space 4 straight n minus 1$

(which depends upon n and is therefore not a constant)

Hence, the given sequence is not an A.P.

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12.

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

1001 Views

13.

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

(i) purely real (ii) purely imaginary?

819 Views

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?

384 Views

15.

Determine the number of terms in an A.P. 3, 8, 13, .......253. Also, find 12th term from the end.

509 Views

16.

Find the 2nd term and the rth term of an A.P. whose 6th term is 12 and 8th term is 22.

484 Views

17.

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.

675 Views

Long Answer Type

18.

In an A.P., the mth term is $1 over straight n$ and the nth term is $1 over straight m comma$ find the (mn)th term.

107 Views

Short Answer Type

19.

If m times the mth term is equal to n times the nth term of an A.P. Prove that (m + w)th term of an A.P. is zero.

280 Views

20.

If (m + l)th term of an A.P. is twice the (n + l)th term. Prove that (3m + l)th term is twice the (m + n + l)th term.

105 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

11. Show that the sequence defined by is not an A.P.

Long Answer Type

Short Answer Type

11.
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.