Question

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

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

Short answer

An equation for the nth term of the arithmetic sequence is $a_n=-2n-1$.

Step-by-step solution

Step 1. Given Information.

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

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Here the first term is $a_1=-3$

The difference between the first two terms is $(-5)-(-3)=-5+3=-2$

The difference between the next two terms is $(-7)-(-5)=-7+5=-2$

Hence, the common difference is $d=-2$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=-3+(n-1)(-2)\\ a_n=-3-2n+2\\ a_n=-2n-1\end{array}$

Step 3. Conclusion.

Hence, an equation for the nth term of the arithmetic sequence is $a_n=-2n-1$.