Write the first five terms of the following sequences:1) ( ( − 1 ) n n 2 n + 1 ) 2) ( 4 + ( − 1 ) n )3) x 1 = 1 , x n + 1 = 3 x n + 14) ( 3 , 3 , 3 , . . . )

Question

Write the first five terms of the following sequences:1)   (            (      −      1              )        n            n              2      n      +      1        ) 2)   (  4  +  (  −  1      )    n    )3)       x    1    =  1  ,      x          n      +      1        =  3      x          n        +  14)   (  3  ,  3  ,  3  ,  .  .  .  )

Lilliana Burton · Accepted Answer

1)   (            (      −      1              )        n            n              2      n      +      1        )Let       S    n    =  [            (      −      1              )        n            n              2      n      +      1        ]      S    1    =  [            (      −      1              )        1            1              2      (      1      )      +      1        ]  =            −      1              2      +      1        =            −      1        3        S    2    =  [            (      −      1              )        2            2              2      (      2      )      +      1        ]  =            1      (      2      )              4      +      1        =      2    5        S    3    =            (      −      1              )        3            3              2      (      3      )      +      1        =            −      1      (      3      )              6      +      1        =            −      3        7        S    4    =            (      −      1              )        4            4              2      (      4      )      +      1        =      4          8      +      1        =      4    9        S    5    =            (      −      1              )        5            5              2      (      5      )      +      1        =            −      5              10      +      1        =            −      5        11   2)   (  4  +  (  −  1      )    n    )Let       S    n    =  (  4  +  (  −  1      )    n    )      S    1    =  (  4  +  (  −  1      )    1    )  =  (  4  −  1  )  =  3      S    2    =  (  4  +  (  −  1      )    2    )  =  (  4  +  1  )  =  5      S    3    =  (  4  +  (  −  1      )    3    )  =  (  4  −  1  )  =  3      S    4    =  (  4  +  (  −  1      )    4    )  =  (  4  +  1  )  =  5      S    5    =  (  4  +  (  −  1      )    5    )  =  (  4  −  1  )  =  33)       x    1    =  1  ,      x          n      +      1        =  3      x          n        +  1      x    1    =  1      x          n      +      1        =  3      x          n      +      1            x    1    =  2      x    2    =  3      x    1    +  1  =  3  (  1  )  +  1  =  3  +  1  =  4      x    3    =  3      x    2    +  1  =  3  (  4  )  +  1  =  12  +  1  =  13      x    4    =  3      x    3    +  1  =  3  (  13  )  +  1  =  39  +  1  =  40      x    5    =  3      x    4    +  1  =  3  (  40  )  +  1  =  120  +  1  =  121

Summer Bradford · Accepted Answer

(4) Given:   (  3  ,  3  ,  3  ,  .  .  .  )      S    1    =  3      S    2    =  3      S    3    =  3      S    4    =  3      S    5    =  3

Write the first five terms of the following sequences: 1) ( ( &#x2212

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