A matchstick's pattern of trapeziums is shown. They are not separate and two neighboring trapeziums have a common matchstick. Can you find the rule for this pattern that gives the number of matchsticks in terms of the number of trapeziums ( where $x$ represents the number of trapeziums)?

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Solution

According to the figure ,(on counting)
1 trapezium requires number of matchsticks $= 5$
2 trapeziums ( having 1 common matchstick ) require number of matchsticks $= 9$
3 trapeziums ( having 2 common matchsticks ) require number of matchsticks $= 13$
Now, if we remove 1 common matchstick from each figure ( and add it separately) , then the remaining make multiples of 4 , i.e , 4,8,12….
So, the required equation can be $= (4 n + 1)$
(where $n$ is the number of trapeziums)

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A matchstick's pattern of trapeziums is shown. They are not separate and two neighboring trapeziums have a common matchstick. Can you find the rule for this pattern that gives the number of matchsticks in terms of the number of trapeziums ( where x represents the number of trapeziums)?

A matchstick's pattern of trapeziums is shown. They are not separate and two neighboring trapeziums have a common matchstick. Can you find the rule for this pattern that gives the number of matchsticks in terms of the number of trapeziums ( where $x$ represents the number of trapeziums)?