Chapter 12: Q. 20 (page 838)

In Problems 20 and 21, find a general formula for each arithmetic sequence
7th term is 31;
20th term is 96

Short Answer

Expert verified

The general formula of the sequence is : $a_{n} = 5 n - 4$

Step by step solution

Step 1. Given information

In an arithmetic sequence :

$a_{7} = 31 a_{20} = 96$

Let $a$ is the first term and $d$ is the common difference of the sequence.

Step 2. Make two equations of a and d

According to the given condition,

$a_{7} = 31 a + (7 - 1) d = 31$

$a + 6 d = 31$ ........... equation (1)

$a_{20} = 96 a + (20 - 1) d = 96$ .

$a + 19 d = 96$ ...............equation (2)

Step 3. Solve equations.

Substract equation (1) from (2)

$(a + 19 d) - (a + 6 d) = 96 - 31 19 d - 6 d = 65 13 d = 65 d = \frac{65}{13} d = 5$

Substitute value of $d$ in equation (1)

$a + 6 \times 5 = 31 a + 30 = 31 a = 31 - 30 a = 1$

Step 4. General formula for sequence.

Substitute values of $a$ and $d$ in general formula of arithmetic sequence.

$a_{n} = a + (n - 1) d a_{n} = 1 + (n - 1) 5 a_{n} = 1 + 5 n - 5 a_{n} = 5 n - 4$

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 20 and 21, find a general formula for each arithmetic sequence
7th term is 31;
20th term is 96

Short Answer

Step by step solution

Step 1. Given information

Step 2. Make two equations of a and d

Step 3. Solve equations.

Step 4. General formula for sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Applied Mathematics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 20 and 21, find a general formula for each arithmetic sequence7th term is 31;20th term is 96

Short Answer

Step by step solution

Step 1. Given information

Step 2. Make two equations of a and d

Step 3. Solve equations.

Step 4. General formula for sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Applied Mathematics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 20 and 21, find a general formula for each arithmetic sequence
7th term is 31;
20th term is 96