Answer to Question #245700 in Algebra for dizzo

Question

The first term of a geometric progression is √ 3+1 and the sum of the first three

terms is 3( √ 3-1) . Find the common ratio of the progression.

(4marks).

Answer 1

$$a=\sqrt{3}-1$$

$$a+ar+ar^2=3(\sqrt{3}-1)$$

$$a(1+r+r^2)=3(\sqrt{3}-1)$$

$$(\sqrt{3}-1)(1+r+r^2)=3(\sqrt{3}-1)$$

$$1+r+r^2=3$$

$$r^2+r-2=0$$

$$r(r-1)+2(r-1)=0$$

$$(r+2)(r-1)=0$$

$$r_1=-2, r_2=1$$

The common ratio of the progression is $-2$ or the common ratio of the progression is $1.$

If we take that $r\not=0, r\not=1,$ then the common ratio of the progression is $-2$.