Chapter 3: Q23. (page 205)

Determine whether each sequence is an arithmetic sequence. If it is,state the common difference.
$0.75, 1.5, 3, 6, 12, .....$

Short Answer

Expert verified

The given sequence is not an arithmetic sequence.

Step by step solution

Step 1. State the concept of arithmetic sequence.

In anArithmetic Sequencethe difference between one term and the next is a constant.

The nthterm of the Arithmetic sequence is given by the formula,

$a_{n} = a + (n - 1) d d = a_{2} - a_{1}$

Where, $a_{1} = a =$ first term and $d =$ common difference.

Step 2. Find the common difference of corresponding terms.

The common difference between the corresponding terms are calculated as follows.

$d = a_{2} - a_{1} = 1.5 - 0.75 = 0.75 d = a_{3} - a_{2} = 3 - 1.5 = 1.5 d = a_{4} - a_{3} = 6 - 3 = 3 d = a_{5} - a_{4} = 12 - 6 = 6$

Step 3. State the conclusion.

Note that the common difference of each corresponding terms are different.

Thus, the given sequence is not an arithmetic sequence.

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Determine whether each sequence is an arithmetic sequence. If it is,state the common difference.
$0.75, 1.5, 3, 6, 12, .....$

Short Answer

Step by step solution

Step 1. State the concept of arithmetic sequence.

Step 2. Find the common difference of corresponding terms.

Step 3. State the conclusion.

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Determine whether each sequence is an arithmetic sequence. If it is,state the common difference.0.75,1.5,3,6,12,.....

Short Answer

Step by step solution

Step 1. State the concept of arithmetic sequence.

Step 2. Find the common difference of corresponding terms.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether each sequence is an arithmetic sequence. If it is,state the common difference.
$0.75, 1.5, 3, 6, 12, .....$