How do you write the first five terms of the sequence defined recursively a 1 = 6 , a k + 1 = a k + 2 , then how do you write the nth term of the sequence as a function of n?

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How do you write the first five terms of the sequence defined recursively             a      1        =    6    ,          a              k        +        1              =          a      k        +    2  , then how do you write the nth term of the sequence as a function of n?

Vaughn Greer · Accepted Answer

As             a              k        +        1              =          a      k        +    2   and             a      1        =    6              a      2        =          a      1        +    2    =    6    +    2    =    8              a      3        =          a      2        +    2    =    8    +    2    =    10              a      4        =          a      3        +    2    =    10    +    2    =    12  and             a      5        =          a      4        +    2    =    12    +    2    =    14  and hence first five terms are {6,8,10,12,14}As             a              k        +        1              =          a      k        +    2  , each term is 2 more than previous termit is an arithmetic sequence with first term as             a      1       and common difference d and hence             n              t        h             term is            a      n        =          a      1        +          (      n      -      1      )        d   and hence             n              t        h             term of the sequence is            a      n        =    6    +          (      n      -      1      )        ×    2    =    6    +    2    n    -    2    =    2    n    +    4

How do you write the first five terms of the sequence defined recursively a_1=6,a_(k+1)=a_k+2, then how do you write the nth term of the sequence as a function of n?

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