/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Find the next term in list. \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 11

Find the next term in list. \(4,8,12,16,20, \dots\)

Short Answer

Expert verified
The next term in the sequence is 24.

Step by step solution

01

Identify the Pattern

Look at the sequence provided: 4, 8, 12, 16, 20, ... Notice that each term increases by a specific amount from the previous term. This indicates an arithmetic sequence.
02

Determine the Common Difference

Calculate the difference between consecutive terms. Subtract any term from the term that follows it, e.g., 8 - 4 = 4, 12 - 8 = 4. The common difference (d) is 4.
03

Use the Formula for the Next Term

In an arithmetic sequence, the next term can be found using the formula: next term = last term + common difference. Here, the last term is 20.
04

Calculate the Next Term

Add the common difference to the last term: 20 + 4 = 24.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Common Difference
In the realm of arithmetic sequences, the common difference is a crucial element. It is the constant value that separates one term from the next in the sequence.
To find the common difference, you simply subtract any term from the one following it. For example, in the sequence 4, 8, 12, 16, 20, each term increases by 4. Hence, the common difference here is 4.
  • Common difference helps in predicting future terms.
  • It ensures that each term follows the pattern uniformly.
  • It can be negative, zero, or positive.
Discovering the common difference is the foundational step in solving and understanding arithmetic sequences.
Identifying Sequence Patterns
Sequence patterns allow us to foresee the arrangement of numbers in a sequence. In arithmetic sequences, each number is derived by adding a fixed amount (common difference) to its predecessor.
Recognizing this pattern is vital to predicting missing terms, like in the sequence 4, 8, 12, 16, 20.
Key points to remember:
  • Identify the uniform increment or decrement.
  • This increase or decrease will help you determine what the sequence will look like as it progresses.
Understanding sequence patterns gives us a framework to solve more complex mathematical challenges beyond basic number prediction.
Connecting to Pre-Algebra Concepts
Arithmetic sequences are a great way to bridge basic mathematical operations and more advanced pre-algebra concepts. They introduce students to the regularities and rules present in mathematics.
Concepts from pre-algebra that link closely to arithmetic sequences include:
  • Understanding order of operations and fundamental arithmetic operations.
  • Applying formulas, such as the one for finding the next term: next term = last term + common difference.
These are building blocks that pave the way for future learning in algebra and beyond, emphasizing the importance of grasping these foundational concepts early on.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Round number to the nearest whole number. 109.3
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.