Chapter 3: Q21. (page 205)

Find the next three terms in each sequence.
$5, 5, 6, 8, 11, 15, ....$

Short Answer

Expert verified

The next three terms are 20, 26 and 33.

Step by step solution

Step 1. Find the common difference of the corresponding terms.

Calculate the common difference between the corresponding terms to find the pattern of the sequence.

$\begin{matrix} a_{2} - a_{1} = 5 - 5 = 0 \\ a_{3} - a_{2} = 6 - 5 = 1 \\ a_{4} - a_{3} = 8 - 6 = 2 \\ a_{5} - a_{4} = 11 - 8 = 3 \\ a_{6} - a_{5} = 15 - 11 = 4 \end{matrix}$

Step 2. Find the trend of the given sequence.

Notice that the difference between each corresponding terms are $0, 1, 2, 3 and 4$ .

Thus the difference is increasing by 1 in each next terms.

Step 3. Find the next three terms.

Following the pattern the next three terms are calculated as follows.

$a_{7} - a_{6} = 5 a_{7} = a_{6} + 5 = 15 + 5 a_{7} = 20 a_{8} - a_{7} = 6 a_{8} = a_{7} + 6 = 20 + 6 a_{8} = 26 a_{9} - a_{8} = 7 a_{9} = a_{8} + 7 = 26 + 7 a_{9} = 33$

Therefore, the next three terms of the given sequence are 20, 26 and 33.

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 next three terms in each sequence.
$5, 5, 6, 8, 11, 15, ....$

Short Answer

Step by step solution

Step 1. Find the common difference of the corresponding terms.

Step 2. Find the trend of the given sequence.

Step 3. Find the next three terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the next three terms in each sequence.5,5,6,8,11,15,....

Short Answer

Step by step solution

Step 1. Find the common difference of the corresponding terms.

Step 2. Find the trend of the given sequence.

Step 3. Find the next three terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the next three terms in each sequence.
$5, 5, 6, 8, 11, 15, ....$