Gp - 80

Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second.

Correct result:

a1 =  2
a2 =  6
a3 =  18
a4 =  54
b1 =  -4
b2 =  12
b3 =  -36
b4 =  108

Solution:

a2=q1⋅ a1=3⋅ 2=6
a3=q1⋅ a2=3⋅ 6=18
a4=q1⋅ a3=3⋅ 18=54
b1=80/(1+q2+q22+q23)=80/(1+(−3)+(−3)2+(−3)3)=−4
b2=q2⋅ b1=(−3)⋅ (−4)=12
b3=q2⋅ b2=(−3)⋅ 12=−36
b4=q2⋅ b3=(−3)⋅ (−36)=108

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