What is the common ratio of the geometric sequence below? –2, 4, –8, 16, –32, ...

The common ratio of the geometric sequence is:

Step-by-step explanation:

A geometric sequence has a constant ratio 'r' and is defined by

where

Given the sequence

Compute the ratios of all the adjacent terms:  

The ratio of all the adjacent terms is the same and equal to

Therefore, the common ratio of the geometric sequence is:

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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