Page 14 - Ganit Kaushal

9. Observe the following pattern and fill in the blank.

1 × 9 = 9, 11 × 99 = 1089
111 × 999 = 110889, 1111 × 9999 = 11108889, and so on.
Then, 111111 × 999999 = _____?
10. Observe the following pattern and fill in the blank in each case.

(a) Identify the missing numbers: 5, 10, 20, 40, _____, _____, _____ .
(b) What comes next in the sequence? 121, 144, 169, 196, _____, _____ .
(c) Identify the rule and find the next two terms: 101, 99, 96, 92, _____, _____ .
11. A pattern follows this rule: Multiply by 2, then subtract 1. If the first number is 3, write the next six
numbers.
12. Ashish saves money every week in the following pattern: `5, `10, `15, `20, …. How much money
will he save in the 8th week?

13. A college staircase has steps numbered in this pattern: 2, 4, 8, 16, …. If the pattern continues, what
will be the number of the 8th step?

14. In point number 5 of section 1.4 above, observe the pattern and write its next 4 steps.

1.5 MORE NUMBER SEQUENCES WITH THEIR GEOMETRIC REPRESENTATION

Number sequences are the most basic and among the most fascinating types of patterns that we study in
mathematics. Now, we give a few important sequences/patterns of numbers.
We will denote the n-th term of a sequence/pattern by T , and {T } (i.e., T with curly brackets) will be the
n
n
n
symbol used to represent a sequence.
Constant Sequence

Consider the sequence {a, a, a, a, ...........}, where ‘a’ is any number.
If we take a = 1, then it is 1, 1, 1, 1, ........... (All 1 numbers)

Can you observe the pattern in the sequence?
Yes, we can observe that each term of the sequence remains the same and is equal to the starting
number.
The above pattern can be well understood with the help of the following figure, involving one green dot for
every term of the pattern. The figure shows the first five terms of the pattern.

(All 1s pattern)
1 1 1 1 1
The constant sequence can also be given by the following formula for its n-th term T as:
n
T = a, for some constant number a; n = 1, 2, 3, 4 ….
n
Sequence of Counting Numbers

Consider the sequence 1, 2, 3, 4, 5 …. (Counting numbers)
Can you observe the pattern here in this sequence?
Yes, we can observe that it starts with 1 and each next term of the sequence is obtained by adding 1
to the previous term. In other words, we can say that each term is the successor of the previous term.

12 Mathematics-6