In a geometric sequence
#displaymath73366#
each succesor term #tex2html_wrap_inline73368# is the result of multiplying a fixed constant wit
#tex2html_wrap_inline73370#. Here is a concrete example, matched up with the natural numbers:
#displaymath73372#
Here the starting point is 3 and the constant is 5. From these, called
starting point and factor, respectively, every other term in the sequence
is determined.
<#31273#>Exercise 23.3.1<#31273#>
Develop the recursive function <#65854#><#31275#>g-fives<#31275#><#65854#>, which consumes a natural
number and recursively determines the corresponding term in the above
geometric sequence. 
Solution<#65855#><#65855#>
<#31281#>Exercise 23.3.2<#31281#>
Develop the non-recursive function <#65856#><#31283#>g-fives-closed<#31283#><#65856#>. It consumes
a natural number and determines the corresponding term in the above
series. Solution<#65857#><#65857#>
<#31289#>Exercise 23.3.3<#31289#>
Develop the function <#65858#><#31291#>seq-g-fives<#31291#><#65858#>, which consumes a natural number
<#65859#><#31292#>n<#31292#><#65859#> and creates the sequence of the first <#65860#><#31293#>n<#31293#><#65860#> terms according
to <#65861#><#31294#>g-fives<#31294#><#65861#> or <#65862#><#31295#>g-fives-closed<#31295#><#65862#>. <#31296#>Hint:<#31296#> Use
<#65863#><#31297#>build-list<#31297#><#65863#>.~ Solution<#65864#><#65864#>
<#31303#>Exercise 23.3.4<#31303#>
Develop <#65865#><#31305#>geometric-series<#31305#><#65865#>. The function consumes two numbers:
<#65866#><#31306#>start<#31306#><#65866#> and <#65867#><#31307#>s<#31307#><#65867#>. Its result is a function that represents
the geometric series whose starting point is <#65868#><#31308#>start<#31308#><#65868#> and whose
factor is <#65869#><#31309#>s<#31309#><#65869#>. For example, <#65870#><#31310#>(geometric-series<#31310#>\ <#31311#>3<#31311#>\ <#31312#>5)<#31312#><#65870#> yields
<#65871#><#31313#>g-fives<#31313#><#65871#> (or <#65872#><#31314#>g-fives-closed<#31314#><#65872#>).~ Solution<#65873#><#65873#>
<#31320#>Exercise 23.3.5<#31320#>
Use <#65874#><#31322#>series<#31322#><#65874#> to determine the sum of the <#65875#><#31323#>g-fives<#31323#><#65875#> sequence
for the bounds 3, 7, and 88.
Use <#65876#><#31324#>series<#31324#><#65876#> to determine the sum of <#65877#><#31325#>(geometric-series<#31325#>\ <#31326#>1<#31326#><#31327#> <#31327#><#31328#>.1)<#31328#><#65877#> for the bounds 3, 7, 88.
Can an infinite geometric series have a sum?~ Solution<#65878#><#65878#>