/*! 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 10 Find the next three terms of eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 10

Find the next three terms of each sequence. \(96,48,24,12, \ldots\)

Short Answer

Expert verified
The next three terms are 6, 3, and 1.5.

Step by step solution

01

Identify the Pattern

Observe the sequence to determine how one term is transformed into the next. Here, each term is half of the previous term. So, the pattern is a division by 2.
02

Apply the Pattern to Find the Next Term

Take the last known term in the sequence, which is 12, and apply the identified pattern. Divide 12 by 2 to find the next term: \( 12 \div 2 = 6 \).
03

Continue the Pattern to the Next Term

Use the newly found term, 6, and apply the pattern again. Divide 6 by 2: \( 6 \div 2 = 3 \).
04

Find the Final Term Using the Pattern

Take the most recent term, which is 3, and divide by 2 again: \( 3 \div 2 = 1.5 \).

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.

Sequence Patterns
Finding patterns in a sequence is like uncovering a secret code! When you look at a sequence of numbers, you're essentially trying to figure out the rule that helps you predict the next numbers. In the example sequence: 96, 48, 24, 12, we notice something fascinating.
  • The numbers are decreasing in a specific manner.
  • Each term is reduced consistently by a specific operation.
This type of sequence, where each number is related by a consistent rule, is known as a geometric sequence. In a geometric sequence, you use a constant called the 'common ratio' to get from one term to the next. If you understand the ratio, you can predict subsequent terms correctly. In this sequence, the pattern relies on dividing by the number 2.
Dividing by 2
"Dividing by 2" is a crucial part of uncovering patterns in certain sequences. In this exercise, dividing by 2 is the key: each term is obtained by dividing the previous one by 2. Let's explore how this works.
  • Begin with the first term, 96. Divide it by 2 to get the next term: 96 divided by 2 equals 48.
  • Continuing, divide 48 by 2 to get 24, and so on.
It's important because this consistent division tells us how the sequence progresses. Essentially, the entire sequence falls apart if this rule is broken. The predictability here is soothing because knowing one term lets you easily find the subsequent ones. Every term acts like a stepping stone, leading you carefully and reliably to the next part of the sequence.
Finding Next Terms
Once you've identified the sequence pattern and understood the role of dividing by 2, you're all set to find the next terms in the sequence. To find the next three terms after 12 in the sequence 96, 48, 24, 12, you simply continue applying "divide by 2":
  • Start with 12: Divide it by 2 to get the next term, which is 6.
  • Then, take 6, divide it by 2, and you get 3.
  • Finally, take 3, divide it by 2 to arrive at 1.5.
Breaking the problem into smaller steps makes the process easier, and understanding the pattern ensures you're applying the right operation each time. As you follow the steps: 12, 6, 3, 1.5, you get a solid grip on how sequences function and how orderly they can be. No guesswork needed, only simple division! Each number follows the previous squarely due to that trusted dividing by 2 rule.

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

Find the value of \(x\). \(12 x=8 x+1\)

Name the slope and \(y\)-intercept of the graph of each equation. \(y=5\)

Graph each equation using the slope and \(y\)-intercept. \(4 x-3 y=-6\)

Construction Some building codes require the slope of a stairway to be no steeper than \(0.88\), or \(\frac{22}{25}\). The stairs in Amad's house measure 11 inches deep and 6 inches high. Do the stairs meet the code requirements? Explain.

Cily Planning In New York City, roads running parallel to the Hudson River are named avenues, and those running perpendicular to the river are named streets. What is the measure of the angle formed at the intersection of a street and an avenue?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

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.