In a geometric series, term number 1=3 and Sum of first 3 terms=21. Determine the common ratio. Thanks!

MapleTheory  May 1, 2017
edited by MapleTheory  May 1, 2017

So your GP is


3, 3r, 3r^2 ....


\(3+3r+3r^2=21\\ 3r^2+3r+3=21\\ r^2+r+1=7\\ r^2+r-6=0\\ (r+3)(r-2)=0\\ r=-3\quad or \quad r=2\\ so\\ 3,-9, 27 \qquad sum=21\\ 3,6, 12 \qquad sum=21\\\)

so the common ratio could be  -3 or  +2

Melody  May 1, 2017

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