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August 3, 2015

August 3, 2015

Posted by **Tosin** on Sunday, November 20, 2011 at 1:52pm.

- Further mathematics -
**Steve**, Sunday, November 20, 2011 at 2:39pmSince 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!

- Further mathematics -
**oladepo oluwatobi**, Sunday, March 3, 2013 at 1:01pm105