Answer to Question #245700 in Algebra for dizzo

Question #245700

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).


1
Expert's answer
2021-10-05T10:58:59-0400
a=31a=\sqrt{3}-1

a+ar+ar2=3(31)a+ar+ar^2=3(\sqrt{3}-1)

a(1+r+r2)=3(31)a(1+r+r^2)=3(\sqrt{3}-1)

(31)(1+r+r2)=3(31)(\sqrt{3}-1)(1+r+r^2)=3(\sqrt{3}-1)

1+r+r2=31+r+r^2=3

r2+r2=0r^2+r-2=0

r(r1)+2(r1)=0r(r-1)+2(r-1)=0

(r+2)(r1)=0(r+2)(r-1)=0

r1=2,r2=1r_1=-2, r_2=1

The common ratio of the progression is 2-2 or the common ratio of the progression is 1.1.


If we take that r0,r1,r\not=0, r\not=1, then the common ratio of the progression is 2-2.


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