Look at the following matchstick pattern of letter $A$ , the $A^{'} s$ are not separate. Two neighbouring $A^{'} s$ have two common matchsticks. Observe the pattern and find the rule that gives the number of matchsticks.

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Solution

in 1st it has 6 matchsticks in 2nd it has 10 matchsticks then it has 14 matchsticks
i.e. in nth figure it has 6+4(n-1) matchsticks
i.e. 2+4n

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Question 11(i)

Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

(a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: if you remove the vertical stick at the end, you will get a pattern of Cs.)

(b) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

Q. Look at the following matchstick pattern of equilateral triangles.The triangles are not separate.Two neighbouring triangles have a common matchstick.Observe the pattern and find the rule that gives the number of matchsticks.

Question 11(i)

Q. Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. What is the rule that gives the number of matchsticks in terms of the number of squares?
(Let the number of squares be x)

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Look at the following matchstick pattern of letter A, the A′s are not separate. Two neighbouring A′s have two common matchsticks. Observe the pattern and find the rule that gives the number of matchsticks.

in 1st it has 6 matchsticks in 2nd it has 10 matchsticks then it has 14 matchsticks i.e. in nth figure it has 6+4(n-1) matchsticks i.e. 2+4n

Look at the following matchstick pattern of letter $A$ , the $A^{'} s$ are not separate. Two neighbouring $A^{'} s$ have two common matchsticks. Observe the pattern and find the rule that gives the number of matchsticks.

in 1st it has 6 matchsticks in 2nd it has 10 matchsticks then it has 14 matchsticks
i.e. in nth figure it has 6+4(n-1) matchsticks
i.e. 2+4n