- #1

chwala

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- Homework Statement:
- If the first, third and sixth term of an arithmetical progression are in geometrical progression, find the common ratio of the geometrical progression.

- Relevant Equations:
- geometric mean

My attempt;

The terms in the arithmetic sequence are ;##[ a, a+2d,a+5d]##.

It follows that;

Common ratio ##r=\dfrac{a+2d}{a}=\dfrac{a+5d}{a+2d}##

##⇒ar+2rd=a+2d+3d##

##ar+2rd=ar+3d##

##ar+2rd-ar=3d##

##2rd=3d##

##r=\dfrac{3d}{2d}=\dfrac{3}{2}##

The solution given on the textbook is ##r=\dfrac{3}{2}##. Seeking alternative method guys.

The terms in the arithmetic sequence are ;##[ a, a+2d,a+5d]##.

It follows that;

Common ratio ##r=\dfrac{a+2d}{a}=\dfrac{a+5d}{a+2d}##

##⇒ar+2rd=a+2d+3d##

##ar+2rd=ar+3d##

##ar+2rd-ar=3d##

##2rd=3d##

##r=\dfrac{3d}{2d}=\dfrac{3}{2}##

The solution given on the textbook is ##r=\dfrac{3}{2}##. Seeking alternative method guys.

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