Page 24 - Ganit Kaushal

Now, we can easily write the 8th term of the pattern. It contains 3 × 8 + 1 = 25 (put n = 8 in T ) matchsticks.
n
This answers (a).

Again, 61 = 3 × 20 + 1, therefore, 20 squares will be formed with the help of 61 matchsticks. This answers (b).
Ex 8. The sequence of powers of 2 is 1, 2, 4, 8, and so on. Start adding up this sequence and then add 1 to
each of the numbers you get. What number sequence do you get?

Sol. Adding up the sequence of powers of 2 starting with 1, we get
1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, …
i.e., 1, 3, 7, 15, …
Now, adding one to each number of the above sequence, we get the following sequence

1 + 1, 3 + 1, 7 + 1, 15 + 1, …
i.e., 2, 4, 8, 16, and so on
Clearly, it is a sequence of powers of 2 again, but this time it starts with two.

Ex 9. In a honeybee colony, the number of male and female bees follows the Fibonacci sequence. If a hive
has 34 female bees, how many male bees might be there?
Sol. The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 34, 55, …
A hive has 34 female bees and 34 is the 8th term of the Fibonacci sequence.
Find the previous Fibonacci term i.e., 7th term: The 7th term in the sequence is 21.

\ There might be 21 male bees in that hive.

Exercise 1.2

1. Give the number and the pictorial representation of the following:
(a) 8th odd number of the odd number sequence.
(b) 10th even number of the even number sequence.
(c) 6th triangular number of the triangular number sequence.

2. Which triangular number is also a square number? Also show it by pictorial representation.
3. What number do you get by adding up and down the first 100 counting numbers? (NCERT)
4. Which sequence do you get when you start to add the all ones sequence up? What sequence do you
get when you add the all ones sequence up and down? (NCERT)

5. Which sequence do you get when you start to add the counting numbers up? Give a pictorial
explanation. (NCERT)
6. Which sequence do you get when you add up pairs of consecutive triangular numbers? Explain it with
a figure. (NCERT)
7. Which term of the sequence of triangular numbers coincides with which term of the sequence of
squares? What is that number?
8. Why are 1, 3, 6, 10, 15, … called triangular numbers? Justify your answer with a pictorial presentation.
9. Why are 1, 4, 9, 16, 25, … called square numbers or squares? Justify your answer with a pictorial
presentation.

10. Why are 1, 8, 27, 64, 125, … called cubes? Justify your answer with pictorial presentation.

22 Mathematics-6