Posted by **Erik** on Sunday, January 29, 2012 at 4:32pm.

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.

- Math -
**Christine**, Monday, January 30, 2012 at 1:19am
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.

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