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.