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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Can you determine how many ways there are to reach the stage by drawing the diagram for 6, 7,
and 8 steps?

Let’s draw a table to summarize the number pattern found in going upstairs to reach the stage.

Number of steps Total number of ways to go upstairs

1 1

2 2

3 3

4 5

5 8

6 13

7 21

8 34

Every next number is the sum of the previous two.

3 = 2 + 1 5 = 2 + 3 8 = 3 + 5 13 = 5 + 8 21 = 8 + 13 34 = 13 + 21

Note: In Fibonacci sequence/ Virahanka numbers, every next number is the sum of the previous two.

Practice Time 1A

1. Complete the patterns:
(a) 4, 8, .........., 16, 20, 24, .......... .

(b) 1, 2, 4, 7, .........., 16, .........., .........., .......... .
2. What numbers complete the given patterns?

(a) 47, 43, 40, 38, 37, 33, .........., .......... .
(b) 100, 90, 81, .........., .........., 60, ..........

3. Multiply 987654321 by 9, 18, 27, ..., 81. Check the pattern of the results obtained.
4. Write down all the possible combinations of climbing up 5 steps when there are no specific conditions
imposed.
5. A professor was living on the first floor of an apartment. The first floor can be reached
by walking up a staircase consisting of 10 steps. The professor usually climbs up by taking either
1 step each time or a maximum 2 steps at a time. In how many ways can the professor reach to
his floor?

Mathematics-6 10