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Chapter 11: Q48. (page 582)

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

-3, -5, -7, -9, ... .

Short Answer

Expert verified

An equation for the nth term of the arithmetic sequence is an=鈭�2n鈭�1.

Step by step solution

01

Step 1. Given Information.

Given arithmetic sequence is -3, -5, -7, -9, ... .

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=鈭�3

The difference between the first two terms is (鈭�5)鈭�(鈭�3)=鈭�5+3=鈭�2

The difference between the next two terms is (鈭�7)鈭�(鈭�5)=鈭�7+5=鈭�2

Hence, the common difference is d=鈭�2

Plugging the values in the formula:

an=a1+(n鈭�1)dan=鈭�3+(n鈭�1)(鈭�2)an=鈭�3鈭�2n+2an=鈭�2n鈭�1

03

Step 3. Conclusion.

Hence, an equation for the nth term of the arithmetic sequence is an=鈭�2n鈭�1.

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