Planimetrics + geometric progression - practice problems
Number of problems found: 12
- Infinite sum of areas
An equilateral triangle A1B1C1 is constructed above the height of the equilateral triangle ABC is constructed as. Above the height of the equilateral triangle A1B1C1 is built triangle A2B2C2, and so on. The procedure is repeated continuously. What is the - Infinity
A square with a side 19 long is an inscribed circle, and the circle is inscribed next square, circle, and so on to infinity. Calculate the sum of the area of all these squares. - Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 16 cm. Calculate: a) the sum of peri - Determine 81988
Determine s5 of the geometric sequence if: a1 + a2 = 10 and a4 - a2 = 120 - Sequence 80450
How many terms does the sequence have if a1=4, Sn=589, d=3, n=? - Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence. - 14 sticks
I was cleaning up my attic recently and found a set of at least 14 sticks which a curious Italian sold me some years ago. Trying hard to figure out why I bought it from him, I realized that the set has the incredible property that there are no three stick - Half of halves
Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the area of the original square is the area of the cut part? - Wire
One pull of wire is reduced by its diameter by 14%. What will be the wire diameter with diameter 19 mm over 10 pulls? - Ray
Light ray loses 1/14 of brightness passing through a glass plate. What is the brightness of the ray after passing through 10 identical plates? - Principal 67954
How long in months will the principal raise 5,000 euros at 5% p.. a. interest 350 euros? - The sequence
Find the nth term of the progression 2,6,12,20...
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