The sum 27

The sum of a geometric progression's second and third terms is six times the fourth term. Find the two possible values of the common ratio.

Correct answer:

r1 =  0.5
r2 =  -0.3333

Step-by-step explanation:

a2+a3=6 a4 a2 + r a2 = 6 r2 a2  1+r=6 r2  1+r=6 r2 6r2+r+1=0 6r2r1=0  a=6;b=1;c=1 D=b24ac=1246(1)=25 D>0  r1,2=2ab±D=121±25 r1,2=121±5 r1,2=0.083333±0.416667 r1=0.5 r2=0.333333333

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