The sum 21

The sum of a geometric progression's 2nd and 3rd terms is six times the 4th term. Find the two possible values of the common ratio B. If the second term is eight, the common ratio is positive. Find the first six terms.

Correct answer:

q1 =  0.6404
q2 =  -0.3904
g1 =  12.4922
g2 =  8
g3 =  5.1232
g4 =  3.2809
g5 =  2.1011
g6 =  1.3455

Step-by-step explanation:

g2+g3 = 4 g4 g2 + q g2 = 4 q2   g2  1+q=4 q2  1+q=4 q2 4q2+q+1=0 4q2q1=0  a=4;b=1;c=1 D=b24ac=1244(1)=17 D>0  q1,2=2ab±D=81±17 q1,2=0.125±0.515388 q1=0.640388203=0.6404 q2=0.390388203

Our quadratic equation calculator calculates it.

g2=8 q>0 q=q1=0.6404  g1=g2/q=8/0.6404=12.4922
g3=q g2=0.6404 8=5.1232
g4=q g3=0.6404 5.1232=3.2809
g5=q g4=0.6404 3.2809=2.1011
g6=q g5=0.6404 2.10111.3455   Verifying Solution:  t2=g2+g34 g4=8+5.12324 3.28090.0004

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