Geometric seq

Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.

Correct answer:

c1 =  81
c2 =  373248
q1 =  3
q2 =  -0.5

Step-by-step explanation:

a+b = 36 b = qa a+c = 90 c = q b a+qa = 36 a + q2 a = 90 a = 36/(1+q) 36+q2 36=90 (1+q)  36+q2 36=90 (1+q) 36q290q54=0 36=2232 90=2325 54=233 GCD(36,90,54)=232=18  2q25q3=0  a=2;b=5;c=3 D=b24ac=5242(3)=49 D>0  q1,2=2ab±D=45±49 q1,2=45±7 q1,2=1.25±1.75 q1=3 q2=0.5 a1=36/(1+q1)=36/(1+3)=9 a2=36/(1+q2)=36/(1+(0.5))=72 c1=a1 q12=9 32=81

Our quadratic equation calculator calculates it.

c2=a2 a22=72 722=373248

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