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Four positive numbers form a geometric sequence. The sum of the four numbers is one more then the common ratio. If the first number is 1/10, find the common ratio.

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Answer:

r=3 where r is the common ratio

Explanation:

The sum of geometric progression for n terms is given by:


S_(n)=a_(1) ( 1-r^(n))/ 1-r, where
a_(1) is the

first term of the series and r is the common ratio.

Now, according to the question, there are four terms and they form a geometric progression. So sum of four terms is given as
S_(4)= 1+r and
a_(1)=1/10.

Also according to the above formula:


S_(4)=a_(1) ( 1-r^(4))/ 1-r

Using the values as given in the question into the above equation we get:


1+r =1/10 ( 1-r^(4))/ 1-r


(1+r)(1-r)=1/10 ( 1-r^(4))

[ Using formula
a^(2) -b^(2) =( a+b)(a-b) ]


(1-r^(2))=1/10 ( 1-r^(2))(1+r^(2))


10=(1+r^(2))


10-1=(r^(2))


√(9)=(r)


r=3
which is the required answer.



User Emson
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