Determine 3938

Determine the quotient and the first member of GP if a3 = 0.39, and a1 + a2 = 0.39.

Correct answer:

q1 =  1.618
q2 =  -0.618
a1 =  0.149
b1 =  1.021

Step-by-step explanation:

a1+a1q=0.39 a1(1+q) = 0.39 a1 = 0.39/(1+q) a1 q2 = 0.39 0.39/(1+q) q2 = 0.39 q2 = 1+q q2q1=0  q2q1=0  a=1;b=1;c=1 D=b24ac=1241(1)=5 D>0  q1,2=2ab±D=21±5 q1,2=0.5±1.118034 q1=1.618033989 q2=0.618033989 q1=1.618

Our quadratic equation calculator calculates it.

a1=0.39/(1+q1)=0.39/(1+1.618)0.149 a2=q1 a1=1.618 0.1490.241 a3=q1 a2=1.618 0.241=10039=0.39 s=a1+a2=0.149+0.241=10039=0.39 a1=0.149
b1=0.39/(1+q2)=0.39/(1+(0.618))1.021 b2=q2 b1=(0.618) 1.0210.631 b3=q2 b2=(0.618) (0.631)=10039=0.39 s=b1+b2=1.021+(0.631)=10039=0.39 b1=1.021

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