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Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) A pattern of letter $ T $ as 
(b) A pattern of letter $ \mathrm{Z} $ as 
(c) A pattern of letter $ \mathrm{U} $ as 
(d) A pattern of letter $ \mathrm{V} $ as 
(e) A pattern of letter $ \mathrm{E} $ as 
(f) A pattern of letter $ S $ as
(g) A pattern of letter A as 
"
To do:
We have to find the rule which gives the number of matchsticks required to make the given matchstick patterns.
Solution:
(a) A pattern of letter \( T \) as
From the figure, we observe that two matchsticks are required to make the letter T.
Therefore, the required pattern is $2n$.
(b) A pattern of letter \( \mathrm{Z} \) as
From the figure, we observe that three matchsticks are required to make the letter Z.
Therefore, the required pattern is $3n$.
(c) A pattern of letter \( \mathrm{U} \) as
From the figure, we observe that three matchsticks are required to make the letter 
.
Therefore, the required pattern is $3n$.
(d) A pattern of letter \( \mathrm{V} \) as
From the figure, we observe that two matchsticks are required to make the letter V.
Therefore, the required pattern is $2n$.
(e) A pattern of letter \( \mathrm{E} \) as
From the figure, we observe that five matchsticks are required to make the letter E.
Therefore, the required pattern is $5n$.
(f) A pattern of letter \( S \) as
From the figure, we observe that five matchsticks are required to make the letter .
Therefore, the required pattern is $5n$.
(g) A pattern of letter A as
From the figure, we observe that six matchsticks are required to make the letter .
Therefore, the required pattern is $6n$.
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