Chapter 12: Q 41. (page 809)

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = 5; a_{n} = 2 a_{n - 1}$

Short Answer

Expert verified

The first five terms of the recursively defined sequence are $5, 10, 20, 40, and 80$ .

Step by step solution

Step 1. Write the given information.

The given recursively defined sequence is:

$a_{1} = 5 a_{n} = 2 a_{n - 1}$

Step 2. Determine the first term and find out the second term.

The first term is $(a_{1}) = 5$ .

Now substitute 2 for nin the given formula $a_{n} = 2 a_{n - 1}$ to get the second term,

$a_{2} = 2 a_{2 - 1} = 2 a_{1} = 2 (5) = 10$

Step 3. Find the 3rd and 4th terms.

Similarly substitute 3, 4 for nin the given formula to get the third and fourth term,

$a_{3} = 2 a_{3 - 1} = 2 a_{2} = 2 (10) = 20 a_{4} = 2 a_{4 - 1} = 2 a_{3} = 2 (20) = 40$

Step 4. Find the 5th term.

Now substitute 5 for nin the given formula to get the 5th term,

$a_{5} = 2 a_{5 - 1} = 2 a_{4} = 2 (40) = 80$

Therefore, the first five terms are $5, 10, 20, 40, 80$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = 5; a_{n} = 2 a_{n - 1}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the first term and find out the second term.

Step 3. Find the 3rd and 4th terms.

Step 4. Find the 5th term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.a1=5;an=2an-1

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the first term and find out the second term.

Step 3. Find the 3rd and 4th terms.

Step 4. Find the 5th term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = 5; a_{n} = 2 a_{n - 1}$