Question #297145

The sum of the first 3 terms of geometric sequence is 189 and the sum of the first 6 terms is 182.


1
Expert's answer
2022-02-14T16:56:06-0500
b1+b1r+b1r2=189b_1+b_1r+b_1r^2=189

b1+b1r+b1r2+b1r3+b1r4+b1r5=182b_1+b_1r+b_1r^2+b_1r^3+b_1r^4+b_1r^5=182



b1(1+r+r2)=189b_1(1+r+r^2)=189

b1r3(1+r+r2)=7b_1r^3(1+r+r^2)=-7

r3=7189r^3=-\dfrac{7}{189}

r=13r=-\dfrac{1}{3}

b1(1+(13)+(13)2)=189b_1(1+(-\dfrac{1}{3})+(-\dfrac{1}{3})^2)=189

b1=189(9)7b_1=\dfrac{189(9)}{7}

b1=243b_1=243

b1=243,r=13b_1=243, r=-\dfrac{1}{3}

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