Heez A. Wasure is hanging clothes out on the clothesline to dry. Heez places one

Question

Heez A. Wasure is hanging clothes out on the clothesline to dry. Heez places one clothespin in the middle and two on the sides of each shirt. He links all of the shirts together so that he conserves clothespins. In the following picture he uses seven clothespins for three shirts. a. How many clothespins would he need for 1 shirt? 2 shirts? 4 shirts? 5 shirts? 10 shirts? 11 shirts? 23 shirts? 76 shirts? 131 shirts? (He has a very long clothesline.) b. Write a recursive rule describing the clothespin pattern. c. Write an explicit rule representing the clothespin pattern. d. Suppose that Heez used 77 clothespins for one line of shirts. How many shirts did he hang out to dry?

Explanation / Answer

a) heez is using one pin in the centre and two pins on sides of each shirt

so for 1 shirt he will use 3 pins

2 shirts he will use 5 pins

4 shirts he will use 9 pins

so there is arithmetic progression in this pattern

An = 3 + (23-1 ) 2

An = 47 pins for 23 shirts

b) recursive rule of arithmetic sequence is given by

An = An-1 + d

d in this case is 2

An = An-1 + 2

c) explicit formula is given by a1 + d(n-1)

An = 3 + 2 (n-1)

d) if heez used 77 clothespin

77 = 3 + 2 ( n-1 )

subtracting 3 from both sides

74 = 2n - 2

adding 2 on both sides

76 = 2n

n = 76/2 = 38

so , he needs 77 pins for 38 shirts

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