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Write the first five terms of each of the sequences whose nth terms are :

$straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n squared plus 5 right parenthesis over denominator 4 end fraction$

815 Views

Write the first five terms of the sequence whose nth terms are:

$straight a subscript straight n space equals space left parenthesis negative 1 right parenthesis to the power of straight n minus 1 end exponent space 5 to the power of straight n plus 1 end exponent$

488 Views

Find the indicated terms in the following sequence whose nth terms are :

$space space straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n minus 2 right parenthesis over denominator straight n plus 3 end fraction$

662 Views

Find the indicated terms in the following sequence whose nth terms are:

$straight h left parenthesis straight n right parenthesis space equals space fraction numerator straight n squared plus 2 straight n over denominator 2 straight n end fraction semicolon space straight h left parenthesis straight n minus 1 right parenthesis comma space straight h left parenthesis 16 right parenthesis$

436 Views

The Fibonacci sequence is defined by

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Find $fraction numerator straight a subscript straight n plus 1 over denominator straight a subscript straight n end fraction$ , for n = 1, 2, 3, 4, 5.

518 Views

6.
Find the first six terms of the sequence whose first term is 1 and whose (n+l)th term is obtained by adding n to the nth term.

Let $straight t subscript straight n$ denote the nth term

               $straight t subscript 1 space end subscript space equals space 1$

According to given equation $straight t subscript straight n plus 1 end subscript space equals space straight t subscript straight n plus straight n$                         ...(i)

Putting n = 1 in (i), we get          $straight t subscript 1 plus 1 end subscript space equals space straight t subscript 1 plus 1 space equals space 1 plus 1 space equals space 2$       $rightwards double arrow space straight t subscript 2 space equals space 2$

Putting n = 2 in (i), we get          $straight t subscript 2 plus 1 end subscript space equals space straight t subscript 2 plus 2 space equals space 2 plus 2 space equals space 4$    $space space rightwards double arrow space space straight t subscript 3 space equals space 4$

Putting n = 3 in (i), we get          $straight t subscript 3 plus 1 end subscript space equals space straight t subscript 3 plus 3 space equals space 4 plus 3 equals 7$       $space space rightwards double arrow space space space space straight t subscript 4 space equals space 7$

Putting n = 4 in (i), we get         $straight t subscript 4 plus 1 end subscript space equals space straight t subscript 4 plus 4 space equals space 7 space plus space 4 space equals space 11$     $rightwards double arrow space straight t subscript 5 equals 11$

Putting n = 5 in (i), we get        $straight t subscript 5 plus 1 end subscript space equals space straight t subscript 5 space plus space 5 space equals space 11 space plus space 5 space equals space 16$    $rightwards double arrow space straight t subscript 6 space equals space 16$

580 Views

Long Answer Type

Consider the sequence defined by t_n = an² + bn + c. If t₂ = 3, t₄ = 13 and t₇ = 113, show that 3t_n = 17n² – 87n + 115

564 Views

Short Answer Type

Write first five terms of the following sequence and obtain the corresponding series.

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191 Views

Write first five terms of the following sequence and obtain the corresponding series.

$straight a subscript 1 space equals space straight a subscript 2 space equals space 2 comma space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript space minus space 1$ , n>2

211 Views

10.

Show that the sequence $space space open curly brackets straight t subscript straight n close curly brackets$ defined by $straight t subscript straight n space equals space nA space plus space straight B$ (where A and B are constant) is an A.P. with common difference A.