How do you express the sequence below as a recursively defined function 4, 11, 25, 53, 109,...?

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Everett Mclaughlin · Accepted Answer

Generally the functions are defined explicitly by a formula in terms of the variable, say x.We can also define functions recursively: in terms of the same function of a smaller variable building on itself and in the case of sequences, this is generally the number of the term.For example here, first term is             a      1        =    4  .Observe that second term             a      2        =    11   is obtained by adding 7 to first termand third term             a      3        =    25   obtained by adding 14 to second term.Hence we can say             a      1        =    4              a      2        =    4    +    7          (      2      -      1      )        =    11  and             a      3        =          a      2        +    7          (      3      -      1      )        =    11    +    7    ×    2    =    21  Hence we can say             a      n        =          a              n        -        1              +    7          (      n      -      1      )      , where             a      1        =    4

How do you express the sequence below as a recursively defined function 4, 11, 25, 53, 109,...?

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