Page 4 - CH-1 -(PATTERNS IN MATHEMATICS) -WS

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

12 What happens when you start to add up hexagonal numbers, i.e., take 1, 1 + 7, 1 + 7 + 19,
1 + 7 + 19 + 37……? Which sequence do you get? Can you explain it using a picture of a
cube?

13 What happens when you add up pairs of consecutive triangular numbers? That is, take 1
+ 3, 3 + 6, 6 + 10, 10 + 15……...? Which sequence do you get? Why?

14 Give a diagrammatic representation of triangular numbers.

15 A honey comb follows a hexagonal pattern. If the first row has 1 cell, second row has 7
cells, third row has 19 cells, then how many will be in the 4 row?
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AN 1. True 2. False 3.True 4. (b) 12100 5. (a)399 6. 390 7.Number theory
S
8.(i)(c) 5, 10, 15, 20, 25, …(ii) (b) 24 (iii) (c) 0, 1, 1, 2, 3 …
(iv) An arithmetic sequence has the same difference between each number, while a
geometric sequence has the same ratio between numbers. In arithmetic, you add a
number each time; in geometric, you multiply by a number each time.

(v) Number sequences help us understand patterns in nature, finance, and technology.
For example,
the Fibonacci sequence appears in how leaves are arranged on a stem.

9.(i) Regular Polygons (ii)Complete graphs (iii)Stacked Triangles (iv) Stacked Squares
(v)Koch Snowflake.

10. (d) Assertion is false and the reason is true.

11. (a) Both A and R are true and R is the correct explanation of A.

12. Hexagonal No. are: 1, 7, 19, 37,……….
Let us add them:
1 = 1 (third power of 1)
3
1 + 7 = 8 = 2 × 2 × 2 = 2 (third power of 2)
3
1 + 7 + 19 = 27 = 3 × 3 × 3 = 3 (third power of 3)
3
1 + 7 + 19 + 37 = 64 = 4 × 4 × 4 = 4 (third power of 4)
3
1 + 7 + 19 + 37 + 61 = 125 = 5 × 5 × 5 = 5 (third power of 5)
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