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Permutations And Combinations

Question
CBSEENMA11012962

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

WiredFaculty for all n>1

Solution

Here, WiredFaculty
Now,               straight a subscript straight n space equals space 3 straight a subscript straight n minus 1 end subscript space plus space 2                               ...(i)  (for n>1)
Putting  n = 2 in (i), we get straight a subscript 2 space equals space 3 straight a subscript 1 space plus space 2 space equals space 3 space left parenthesis 3 right parenthesis space plus space 2 space equals space 9 space plus space 2 space equals space 11
Putting n = 3 in (i), we get straight a subscript 3 space equals space 3 straight a subscript 2 space plus space 2 space equals space 3 space left parenthesis 11 right parenthesis space plus space 2 space equals space 33 space plus space 2 space equals space 35
Putting n =4 in (i), we get straight a subscript 4 space equals space 3 straight a subscript 3 space plus space 2 space equals space 3 space left parenthesis 35 right parenthesis space plus space 2 space equals space 105 space plus space 2 space equals space 107
Putting n = 5 in (i), we get straight a subscript 5 equals space 3 straight a subscript 4 plus space 2 space equals space 3 space left parenthesis 107 right parenthesis space plus space 2 space equals space 321 space plus space 2 space equals space 323.
The corresponding series is : 3 + 11 + 35 + 107 + 323 + ..........

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