Cody is designing a pattern for a wood floor the length of the pieces of wood are 1 1/2 inches 1 13/16 inches and 2 1/8 inches what is the length of the fifth piece of wood if the pattern continues

The length of the fifth piece is 2 3/4 inches.

Given:
1st piece of wood = 1 1/2 inches
2nd piece of wood = 1 13/16 inches
3rd piece of wood = 2 1/8 inches

f(n) = 1st term + common difference(n-1)

To get the common difference, we need to deduct the fraction from its preceding fraction.

1st piece: 1 1/2 = (2*1 + 1)/2 = 3/2
2nd piece: 1 13/16 = (16*1+13)/16 = 29/16
3rd piece: 2 1/8 = (8*2+1)/8 = 17/8

29/16 - 3/2 = 29/16 - (3/2 * 8/8) = 29/16 - 24/16 = (29-24)/16 = 5/16
17/8 - 29/16 = (17/8 *2/2) - 29/16 = 34/16 - 29/16 = (34-29)/16 = 5/16

Find: 5th piece's measurement
1st term : 1 1/2 or 3/2
common difference : 5/16

f(5) = 3/2 + 5/16 (5-1)
      = 3/2 + 5/16 (4)
      = 3/2 + (5*4)/16
      = 3/2 + 20/16
      = (3/2 * 8/8) + 20/16
      = 24/16 + 20/16
      = (24 + 20)/16
f(5) = 44/16
f(5) = 2 12/16 simplified to 2 3/4 inches.

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