Page 215 - Start Up Mathematics_6

5. Use the general term of the following pattern and complete the table as indicated:

S. No. Pattern General term Term number Value of the term
1. 2, 4, 6, 8, 10, ... 2n 50th
2. 2, 5, 8, 11, 14, ... 3n – 1 21st
3. 9, 13, 17, 21, 25, ... 4n + 5 36th
4. 11, 19, 27, 35, ... 8n + 3 69th
5. 4, 13, 22, 31, ... 9n – 5 100th
6. Observe the following pattern of quadrilaterals made with matchsticks and complete the
table. Also, write the generalized term.

Number of quadrilaterals 1 2 3 4 5 10 ... n
Number of matchsticks 5 9 13 … … … … ...
7. Observe the following pattern of overlapping triangles made with matchsticks and complete
the table. Also, write the general rule that gives the number of matchsticks.

Number of triangles 1 2 3 4 5 10 ... n
Number of matchsticks 6 10 14 … … … … ...

Use of Variables
We have already learnt certain rules in Arithmetic and Geometry. Here we will realize that these
become easier to express using variables.

Common Rules in Arithmetic
As learnt earlier, some of the properties in whole numbers are mentioned using literals or variables.

1. Commutative Property for Addition of Two Numbers
Let a and b be two variables, which can attain any number value.

Then, a + b = b + a.
2. Commutative Property for Multiplication of Two Numbers

Let a and b be two variables, which can attain any number value.
Then, a × b = b × a.
3. Distributive Property of Numbers

Let a, b and c be three variables, which can attain any number value.
Then, a × (b + c) = a × b + a × c.

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