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Algebra-->View question

Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.-Mathematics-cbse-class 6th-Algebra


(a) A pattern of letter T as 
(b) A pattern of letter Z as 
(c) A pattern of letter U as 
(d) A pattern of letter V as 
(e) A pattern of letter E as 
(f) A pattern of letter S as 
(g) A pattern of letter A as 


Asked On2017-12-21 15:46:01 by:leo

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a) Let us write the letter n for the number of T’s.
If one T is made, n = 1; if two T’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 2 matchsticks are required for making one letter T. So,
For n = 1, the number of matchsticks required is 2 × 1 = 2. [T]
For n = 2, the number of matchsticks required is 2 × 2 = 4. [TT]
For n = 3, the number of matchsticks required is 2 × 3 = 6. [TTT] …
For n number of T’s, the number of matchsticks requires is = 2 × n = 2n
b) Let us write the letter n for the number of Z’s.
If one Z is made, n = 1; if two Z’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 3 matchsticks are required for making one letter Z. So,
For n = 1, the number of matchsticks required is 3 × 1 = 3. [Z]
For n = 2, the number of matchsticks required is 3 × 2 = 6. [ZZ]
For n = 3, the number of matchsticks required is 3 × 3 = 9. [ZZZ]…
For n number of Z’s, the number of matchsticks requires is = 3 × n = 3n
c) Let us write the letter n for the number of U’s.
If one U is made, 𝑛 = 1; if two U’s are made, 𝑛 = 2 and so on;
thus, 𝑛 can be any natural number 1, 2, 3, 4, 5 …
We see that 3 matchsticks are required for making one letter U. So,
For n = 1, the number of matchsticks required is 3 × 1 = 3. [U]
For n = 2, the number of matchsticks required is 3 × 2 = 6. [UU]
For n = 3, the number of matchsticks required is 3 × 3 = 9. [UUU]…
For n number of U’s, the number of matchsticks requires is = 3 × n = 3n
d) Let us write the letter n for the number of V’s.
If one V is made, n = 1; if two V’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 2 matchsticks are required for making one letter V. So,
For n = 1, the number of matchsticks required is 2 × 1 = 2. [V]
For n = 2, the number of matchsticks required is 2 × 2 = 4. [VV]
For n = 3, the number of matchsticks required is 2 × 3 = 6. [VVV] …
For n number of V’s, the number of matchsticks requires is = 2 × n = 2n
e) Let us write the letter n for the number of E’s.
If one E is made, n = 1; if two E’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 5 matchsticks are required for making one letter E. So,
For n = 1, the number of matchsticks required is 5 × 1 = 5. [E]
For n = 2, the number of matchsticks required is 5 × 2 = 10. [EE]
For n = 3, the number of matchsticks required is 5 × 3 = 15. [EEE] …
For n number of E’s, the number of matchsticks requires is = 5 × n = 5n
f) Let us write the letter 𝑛 for the number of S’s.
If one S is made, n = 1; if two S’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 5 matchsticks are required for making one letter S. So,
For n = 1, the number of matchsticks required is 5 × 1 = 5. [S]
For n = 2, the number of matchsticks required is 5 × 2 = 10. [SS]
For n = 3, the number of matchsticks required is 5 × 3 = 15. [SSS] …
For n number of S’s, the number of matchsticks requires is = 5 × n = 5n
g) Let us write the letter n for the number of A’s.
If one A is made, n = 1; if two A’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5 …
We see that 6 matchsticks are required for making one letter A. So,
For n = 1, the number of matchsticks required is 6 × 1 = 6. [A]
For n = 2, the number of matchsticks required is 6 × 2 = 12. [AA]
For n = 3, the number of matchsticks required is 6 × 3 = 18. [AAA] …
For n number of A’s, the number of matchsticks requires is = 6 × n = 6n

Answerd on:2017-12-26 Answerd By:Purnima

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