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 $-2$.