Number Sequence and Patterns|| Exercise 2.1 complete || class 8th Math || #newsyllabus2022_23

Summary

This video script explains the concept of number sequences, focusing on both finite and infinite sequences. It covers how to identify, complete, and analyze number patterns, such as sequences with consistent additions or multiplications. Examples include sequences like 28, 24, 20, 16, where numbers decrease by 4, and others where multiplication patterns (such as multiplying by 3) are applied. The script also delves into practical exercises for completing sequences by identifying the operations required to link terms. This educational content provides a detailed, step-by-step guide to understanding and working with number sequences.

Takeaways

• 😀 A sequence consists of numbers arranged in a particular order, with each number having a specific relationship to the previous one.
• 😀 A sequence can be infinite, meaning it continues indefinitely without a known nth term, or finite, meaning it has a defined end.
• 😀 An infinite sequence is a series of numbers that keeps going on forever, such as 2, 4, 6, 8, and so on.
• 😀 In contrast, a finite sequence ends after a specific number of terms, such as 137, 13, 21, which stops at 21.
• 😀 Arithmetic sequences are common, where numbers are added or subtracted by a constant value, like 28, 24, 20, 16.
• 😀 Identifying the pattern in a sequence is key to completing it, such as subtracting 4 from each term in an arithmetic sequence.
• 😀 Multiplying numbers by a constant, like in the sequence 3, 9, 27, 81, is another common pattern found in sequences.
• 😀 Sequences may also involve a pattern of increasing or decreasing additions, like adding 6, 7, 8, and so on in a sequence.
• 😀 In sequences with missing terms, determining the correct value requires identifying the pattern and performing the necessary operation, such as addition or multiplication.
• 😀 Understanding the structure of a sequence helps predict its future terms and complete it accurately, whether it's based on addition, subtraction, or multiplication.

Q & A

What is the difference between an infinite sequence and a finite sequence?

An infinite sequence goes on forever without a defined last term (e.g., 2, 4, 6, ...), while a finite sequence has a defined last term and does not continue indefinitely (e.g., 137, 13, 21).

How is the sequence 28, 24, 20, 16 formed?

This sequence is formed by subtracting 4 from each term. Starting with 28, subtract 4 to get 24, then subtract 4 again to get 20, and so on.

What is the pattern for the sequence 137, 13, 21?

This sequence is finite, with a known last term (21). The terms appear to be decreasing in a particular pattern, possibly involving subtraction or division.

What operation is applied in the sequence 50, 100, 150?

In this sequence, 50 is added to each term to generate the next term: 50 + 50 = 100, and 100 + 50 = 150.

How do we complete the sequence 3, __, 27?

To complete the sequence, you need to multiply each term by 3. Starting from 3, multiplying by 3 gives 9, and multiplying 9 by 3 gives 27.

What is the pattern in the sequence 11, 17, 24, 32, 41, 51?

The pattern involves adding 6, then 5, then 4, and so on. For example, 11 + 6 = 17, 17 + 7 = 24, 24 + 8 = 32, and so on.

What is the next term in the sequence 2, 4, 6, __?

The next term in this sequence is 8, as it follows a pattern of adding 2 to the previous term.

How is the sequence 77, 66, 55, 44, 33, 22 formed?

This sequence is made by subtracting 11 from each term: 77 - 11 = 66, 66 - 11 = 55, and so on.

What is the role of the three dots (…) in a sequence?

The three dots indicate that the sequence continues indefinitely. It means the pattern goes on forever without a defined last term.

How is the sequence 3, 9, 27, 81, 243, ... created?

This sequence is created by multiplying each term by 3: 3 x 3 = 9, 9 x 3 = 27, 27 x 3 = 81, and so on.