Page 31 - Ganit Kaushal

Assertion Reason Type Questions
A statement of assertion (A) is followed by a statement of reason (R). Choose the correct option out of the
choices given below for each question:
(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.
1. Assertion (A): 15 is a triangular number.
Reason (R): A triangular number can be put in the form of a triangle made up of dots.
2. Assertion (A): 21 is a triangular number.
Reason (R): By taking the difference of two consecutive triangular numbers, we get the sequence of
counting numbers starting with 2.
3. Assertion (A): Adding up the pairs of consecutive triangular numbers gives the sequence of squares
other than 1.
Reason (R): 29 is a hexagonal number.
4. Assertion (A): Adding up the sequence of triangular numbers gives the sequence of cubes.
Reason (R): The number of edges in each shape of the sequence of complete graphs gives the sequence
of triangular numbers.
5. Assertion (A): Hexagonal numbers can be shown by the shape of a hexagon made up of dots.
Reason (R): Adding up the sequence of hexagonal numbers gives the sequence of cubes other than 1.
6. Assertion (A): Koch snowflakes start with an equilateral triangle.
Reason (R): Equilateral triangles have all their angles equal.
7. Assertion (A): The sequence of powers of 2 is 1, 2, 4, 8, 16, and so on.
Reason (R): The nth term of the sequence of powers of 2 is given by 2 n–1 ; n = 1, 2, 3, 4, ……

8. Assertion (A): The 5th hexagonal number is 37.
Reason (R): Every square number is the sum of two consecutive triangular numbers.

Summary of the Chapter

• Among the most basic patterns that occur in mathematics are number sequences.
• Some important examples of number sequences include the counting numbers, odd numbers, even
numbers, square numbers, triangular numbers, cube numbers, Virahānka numbers, and powers of 2.
• Sometimes number sequences can be related to each other in beautiful and remarkable ways. For
Example: adding up the sequence of odd numbers starting with 1 gives square numbers. Adding up
two consecutive triangular numbers gives a sequence of square numbers, etc.
• Visualising number sequences using pictures can help to understand sequences and the relationships
between them.
• Shape sequences are another basic type of pattern in mathematics.
• Some important examples of shape sequences include regular polygons, complete graphs, stacked
triangles and squares, and Koch snowflake iterations. Shape sequences also exhibit many interesting
relationships with number sequences.

Patterns in Mathematics 29