Posted by Erik on Sunday, January 29, 2012 at 4:32pm.
5. The only sequences that are both
arithmetic and geometric are constant
sequences, in which all the terms must
be the same. For us to have a sum of 20,
each term of the sequence must be 5. We
can show this algebraically by solving
the system of equations a + d = ar and
a + 2d = arē where a represents the first term of the sequence, d the common
difference of the arithmetic sequence,
and r the common ratio of the geometric sequence. This system produces the
solution d = 0 and r = 1.
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