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Question

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals


A

1-52

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B

52

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C

5

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D

5-12

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Solution

The correct option is D

5-12


The explanation for the correct option

Let us assume that the first term of the geometric progression is a and the common ratio is r.

Thus, the first three terms of the progression can be given by a, ar and ar2.

It is given that each term equals the sum of the next two terms.

Thus, a=ar+ar2.

a=ar+r21=r+r2r2+r-1=0

The solution to the quadratic equation ax2+bx+c=0 can be given by, x=-b±b2-4ac2a.

Therefore, the solution for the equation r2+r-1=0 is r=-1±12-41-121.

r=-1±1+42r=-1±52

As the progression consists only of positive terms, therefore, the common ratio of the progression, r=5-12.

Hence, (D) is the correct option.


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