Question

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

Answer 1

$$b_1+b_1r+b_1r^2=189$$

$$b_1+b_1r+b_1r^2+b_1r^3+b_1r^4+b_1r^5=182$$

$$b_1(1+r+r^2)=189$$

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

$$r^3=-\dfrac{7}{189}$$

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

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

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

$$b_1=243$$

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