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Chapter 11: Q47. (page 582)

Write an equation for the nth term of each arithmetic sequence.

18, 11, 4, -3, ... .

Short Answer

Expert verified

An equation for the nth term of the arithmetic sequence isan=25鈭�7n .

Step by step solution

01

Step 1. Given Information.

Given arithmetic sequence is 18, 11, 4, -3, ... .

02

Step 2. Calculation.

The nth term of an arithmetic sequence is given by an=a1+(n鈭�1)d.

Here the first term is a1=18

The difference between the first two terms is 11鈭�18=鈭�7

The difference between the next two terms is 4鈭�11=鈭�7

Hence, the common difference is d=鈭�7

Plugging the values in the formula:

an=a1+(n鈭�1)dan=18+(n鈭�1)(鈭�7)an=18鈭�7n+7an=25鈭�7n

03

Step 3. Conclusion.

Hence, an equation for the nth term of the arithmetic sequence is an=25鈭�7n.

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