Chapter 12: Q. 10 (page 816)

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{a_{n}\} = \{4 - 2 n\}$

Short Answer

Expert verified

The solution is $d = - 2$ ; first four terms $= 2, 0, - 2, - 4$ .

Step by step solution

Step 1. Given information

$\{a_{n}\} = \{4 - 2 n\}$

Step 2. Calculation

The first term is $a_{1} = 4 - 2 \cdot 1 = 2$ .

The $n$ th term and the $(n - 1)$ st term of the sequence are-

$a_{n} = 4 - 2 n$ and $a_{n - 1} = 4 - 2 (n - 1) = 4 - 2 n + 2 = 6 - 2 n$

The common difference is -

$d = a_{n} - a_{n - 1} = (4 - 2 n) - (6 - 2 n) = - 2$

Since the difference of any two successive terms is the constant $- 2$ , the sequence $\{a_{n}\}$ is arithmetic.

The first four terms are $2, 0, - 2, - 4$ .

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In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{a_{n}\} = \{4 - 2 n\}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.an=4-2n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Logic and Functions

Applied Mathematics

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Decision Maths

Study anywhere. Anytime. Across all devices.

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{a_{n}\} = \{4 - 2 n\}$