In an arithmetic sequence
#displaymath73358#
each successor term #tex2html_wrap_inline73360# is the result of adding a fixed constant to
#tex2html_wrap_inline73362#. Here is a concrete example, matched up with the natural numbers:
#displaymath73364#
Here the starting point is 3 and the constant is 5. From these two facts,
called <#31199#>starting point<#31199#> and <#31200#>summand<#31200#>, respectively, all other
terms in the sequence can be determined.
<#31203#>Exercise 23.2.1<#31203#>
Develop the recursive function <#65830#><#31205#>a-fives<#31205#><#65830#>, which consumes a natural
number and recursively determines the corresponding term in the above
series.~ 
Solution<#65831#><#65831#>
<#31211#>Exercise 23.2.2<#31211#>
Develop the non-recursive function <#65832#><#31213#>a-fives-closed<#31213#><#65832#>. It consumes
a natural number and determines the corresponding term in the above
series. A non-recursive function is sometimes called a <#31214#>closed form.<#31214#>~ Solution<#65833#><#65833#>
<#31220#>Exercise 23.2.3<#31220#>
Use <#65834#><#31222#>series<#31222#><#65834#> to determine the sum of the <#65835#><#31223#>a-fives<#31223#><#65835#> sequence
for the bounds 3, 7, and 88. Can an infinite arithmetic series have a
sum?~ Solution<#65836#><#65836#>
<#31229#>Exercise 23.2.4<#31229#>
Develop the function <#65837#><#31231#>seq-a-fives<#31231#><#65837#>, which consumes a natural number
<#65838#><#31232#>n<#31232#><#65838#> and creates the sequence of the first <#65839#><#31233#>n<#31233#><#65839#> terms according
to <#65840#><#31234#>a-fives<#31234#><#65840#> or <#65841#><#31235#>a-fives-closed<#31235#><#65841#>. <#31236#>Hint:<#31236#> Use
<#65842#><#31237#>build-list<#31237#><#65842#>.~ Solution<#65843#><#65843#>
<#31243#>Exercise 23.2.5<#31243#>
Develop <#65844#><#31245#>arithmetic-series<#31245#><#65844#>. The function consumes two numbers:
<#65845#><#31246#>start<#31246#><#65845#> and <#65846#><#31247#>s<#31247#><#65846#>. Its result is a function that represents
the arithmetic series whose starting point is <#65847#><#31248#>start<#31248#><#65847#> and whose
summand is <#65848#><#31249#>s<#31249#><#65848#>. For example, <#65849#><#31250#>(arithmetic-series<#31250#>\ <#31251#>3<#31251#>\ <#31252#>5)<#31252#><#65849#>
yields <#65850#><#31253#>a-fives<#31253#><#65850#> (or <#65851#><#31254#>a-fives-closed<#31254#><#65851#>). Similarly,
<#65852#><#31255#>(arithmetic-series<#31255#>\ <#31256#>0<#31256#>\ <#31257#>2)<#31257#><#65852#> produces a function that represents the
series of even numbers.~ Solution<#65853#><#65853#>