posted by Erik on .
A sequence of four integers is both arithmetic and geometric. if the sum of the four numbers is 20, find the first integer in the sequence.
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 = ar² 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.