Question

If there are beads with 24 beads in total, and the first bead has a diameter of .25 inches and each bead increases in circumference by .15 inches each bead, what is the radius of the 24th bead?

Answer 1

1) circumference of the first bead = 0.25 in

2) circumference of the second bead = (0.25 + 0.15) in

3) circumference of the third bead = 0.25 + 0.15*2 in

4) circumference of the nth bead = 0.25 + 0.15 * (n -1) in

5) circumference of the 24th bead = 0.25 + 0.15 * (24 - 1) = 3.7 in

6) circumference = 2π*radius => radius = circumference / (2π)

7) radius of the 24th bead = circumference of the 24th bead / (2π)

radius of the 24th bead = 3.7 inches / (2π) = 0.5889 in ≈ 0.59 in

Answer: 0.59 in