The spiral in the picture is made from 45º right triangles. The smallest triangle (red) has a side length of 1. You can use the Pythagorean theorem to find the length of its hypotenuse. The next (orange) triangle has a side length exactly matching the hypotenuse of the smallest triangle, and so on with the larger triangles of other colors. The lengths of the hypotenuses of all the triangles (starting with the smallest) make a geometric sequence. What is the ratio of the sequence?
Before you try to answer this question, use the Pythagorean theorem to find the length of the first few triangles

Question

The spiral in the picture is made from 45º right triangles. The smallest triangle (red) has a side length of 1. You can use the Pythagorean theorem to find the length of its hypotenuse. The next (orange) triangle has a side length exactly matching the hypotenuse of the smallest triangle, and so on with the larger triangles of other colors. The lengths of the hypotenuses of all the triangles (starting with the smallest) make a geometric sequence. What is the ratio of the sequence?
Before you try to answer this question, use the Pythagorean theorem to find the length of the first few triangles