Chapter 11: Q59. (page 582)

Find the first term in the arithmetic sequence?
$_, 8 \frac{1}{3}, 7, 5 \frac{2}{3}, 4 \frac{1}{3}, ...$
3
$9 \frac{2}{3}$
$10 \frac{1}{3}$
11

Short Answer

Expert verified

B) The first term in the arithmetic sequence is $9 \frac{2}{3}$ .

Step by step solution

Step 1. Given Information.

The given arithmetic sequence is $__, 8 \frac{1}{3}, 7, 5 \frac{2}{3}, 4 \frac{1}{3}, ...$

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $7 - 8 \frac{1}{3} = - 1 \frac{1}{3}$

The difference between the next two terms is $5 \frac{2}{3} - 7 = - 1 \frac{1}{3}$

So, the common difference is $- 1 \frac{1}{3}$ .

The first term is given by:

$\begin{array}{l} a_{1} - 1 \frac{1}{3} = 8 \frac{1}{3} \\ a_{1} = 8 \frac{1}{3} + 1 \frac{1}{3} \\ a_{1} = 9 \frac{2}{3} \end{array}$

Step 3. Conclusion.

Hence, the first term in the arithmetic sequence is $9 \frac{2}{3}$ .

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.

Find the first term in the arithmetic sequence?
$_, 8 \frac{1}{3}, 7, 5 \frac{2}{3}, 4 \frac{1}{3}, ...$
3
$9 \frac{2}{3}$
$10 \frac{1}{3}$
11

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the first term in the arithmetic sequence?_,813,7,523,413,...3923101311

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the first term in the arithmetic sequence?
$_, 8 \frac{1}{3}, 7, 5 \frac{2}{3}, 4 \frac{1}{3}, ...$
3
$9 \frac{2}{3}$
$10 \frac{1}{3}$
11