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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 23 "Sequences -- Quickstart
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 221 "This
 worksheet illustrates the way in which Maple can be used to work with
 sequences.  The following cell defines a sequence representing a bank
 account earning 4 percent interest with an initial deposit of 100 dol
lars.  " }{TEXT 256 23 "Evaluate that cell now." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "InitialVal
ue := 100:\n  Fcn := p -> 1.04 * p:\n\n  bank :=\n     proc(n)\n      \+
  if n = 1 then InitialValue else Fcn(bank(n-1)) \n        fi \n     e
nd:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 143 "Now that Maple \"knows\" how to compute this sequence you can \+
print any of the terms of this sequence by evaluating a cell like the \+
cell below.  " }{TEXT 257 60 "Evaluate that cell now and then go on to
 the following cell." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "bank(10);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 141 "The next cell produces a
 table showing the first 20 terms of this sequence.  Evaluate the next
 cell now and then go on to the following cell." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "for k from \+
1 to 20 \n    do printf(`%4d %10.4f`, k, bank(k));\n    print();\n    \+
od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 90 "Maple can also produce a graph showing this same data.  The fol
lowing cell does the job.  " }{TEXT 258 53 "Evaluate it now and then g
o on to the following cell." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "plot([seq([n, bank(n)], n = \+
1 .. 20)], \n        year = 1 .. 20, title = `Bank Account`);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "No
w you can use these Maple tools to study the sequences in this module.
" }}}}{MARK "0 0 0" 23 }{VIEWOPTS 1 1 0 1 1 1803 }