/*! 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 20 Write a formula for the general ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 20

Write a formula for the general term (the nth term of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7},\) the seventh term of the sequence. $$12,6,3, \frac{3}{2}, \dots$$

Short Answer

Expert verified
The formula for the nth term of the sequence is \(a_{n} = 12 * 0.5^{(n-1)}\), and the seventh term of the sequence is \(a_{7} = 0.1875\)

Step by step solution

01

Find the Common Ratio

To find the common ratio, divide the second term by the first term. So \(r = \frac{6}{12} = 0.5\)
02

Write the formula for the nth term

Now that we know the first term \(a_{1} = 12\) and the common ratio \(r = 0.5\), we can use the general formula for the nth term of a geometric sequence \(a_{n} = a_{1} * r^{(n-1)}\). This gives us \(a_{n} = 12 * 0.5^{(n-1)}\)
03

Find the seventh term

To find the seventh term, substitute \(n = 7\) into the formula: \(a_{7} = 12 * 0.5^{(7-1)} = 12 * 0.5^{6} = 12 * 0.015625 = 0.1875\)

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!

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

Make Sense? In Exercises \(78-81,\) determine whether each statement makes sense or does not make sense, and explain your reasoning. I was able to find the sum of the first 50 terms of an arithmetic sequence even though I did not identify every term.

Exercises \(67-72\) are based on the following jokes about books: \(\cdot\) "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." - Groucho Marx \(\cdot\) "I recently bought a book of free verse. For \(\$ 12\)." \- George Carlin \(\cdot\) "If a word in the dictionary was misspelled, how would we know?" - Steven Wright \(\cdot\) "Encyclopedia is a Latin term. It means 'to paraphrase a term paper." - Greg Ray \(\cdot\) "A bookstore is one of the only pieces of evidence we have that people are still thinking." - Jerry Seinfeld \(\cdot\) "I honestly believe there is absolutely nothing like going to bed with a good book. Or a friend who's read one." \(-\)Phyllis Diller In how many ways can people select their two favorite jokes from these comments about books?

The group should select real-world situations where the Fundamental Counting Principle can be applied. These could involve the number of possible student ID numbers on your campus, the number of possible phone numbers in your community, the number of meal options at a local restaurant, the number of ways a person in the group can select outfits for class, the number of ways a condominium can be purchased in a nearby community, and so on. Once situations have been selected, group members should determine in how many ways each part of the task can be done. Group members will need to obtain menus, find out about telephone-digit requirements in the community, count shirts, pants, shoes in closets, visit condominium sales offices, and so on. Once the group reassembles, apply the Fundamental Counting Principle to determine the number of available options in each situation. Because these numbers may be quite large, use a calculator.

A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.