SOLUTION: A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form an inscribed equilateral triangle, and this process is continued. Find the sum of the peri

Algebra ->  Sequences-and-series -> SOLUTION: A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form an inscribed equilateral triangle, and this process is continued. Find the sum of the peri      Log On


   

Question 751737: A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form an inscribed equilateral triangle, and this process is continued. Find the sum of the perimeters of the triangles if the process is continued without end.
Answer by reviewermath(1029) About Me  (Show Source):
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Perimeter of first triangle: 30 cm
second triangle: 15 cm
third triangle: 7.5 cm
...
nth triangle: 30%280.5%29%5E%28n+-+1%29
...
The sum of an infinite geometric series with first term a%5B1%5D and common ratio r is a%5B1%5D%2F%281+-+r%29 provided |r| < 1.
sum%2830%280.5%29%5E%28n+-+1%29%2C+n=+1%2C+infinity%29 = 30%2F%281+-+0.5%29 = highlight%2860%29 cm.