Posted by Tosin on Sunday, November 20, 2011 at 1:52pm.
Since the two sequences have the same first term, and they sum to 3, they both start with 3/2.
Let the arithmetic sequence be 3/2, 3/2 + d, 3/2 + 2d, ...
Let the geometric sequence be 3/2, 3/2 r, 3/2 r^2, ...
3/2 + d + 3/2 r = 3/2
so, d = -3/2 r
3/2 + 2d + 3/2 r^2 = 6
r = 3 or -1
d = -9/2 or 3/2
AS: 3/2, -3, -15/2, ...
GS: 3/2, 9/2, 27/2, ...
or
AS: 3/2, 3, 9/2, ...
GS: 3/2, -3/2, 3/2, ...
I assume you can make it to the 5th terms of each sequence.
Cool problem!
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