This spreadsheet is set-up in such a way that the starting number of
the sequence can be changed , and thus changing the entire sequence, by
simply changing the number in E2. This is particularly useful when discussing
the ratio of the terms. The spreadsheet is instantly updated by changing
one cell. For the sake of space I only show the first few terms of the sequence.
However, with spreadsheets in the classroom, teachers can show a large part
of the sequence in a relatively short amount of time. This spreadsheet is
particularly useful when discussing the golden ratio. Students can investigate
whether the limit of the ratio is always the same when using different number
to begin the sequence.
If you look closely you will notice that the ratio columes seem to have
the same numbers. If you could view more of this spreadsheet you would see
that the ratios of the terms converge to 1.61803399. This is true for both
sequences and it does not matter what the starting number is .