Question

write an equation that describes the nth term of the arithmetic sequence -2, -1.5, -1, -0.5, 0, 0.5, ....

Explanation:

Step1: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.

Step2: Identify \( a_1 \) and \( d \)

For the sequence \(-2, -1.5, -1, -0.5, 0, 0.5, \dots\), the first term \( a_1=-2 \).
To find the common difference \( d \), we subtract the first term from the second term: \( d=-1.5 - (-2)= -1.5 + 2 = 0.5=\frac{1}{2} \).

Step3: Substitute \( a_1 \) and \( d \) into the formula

Substitute \( a_1 = -2 \) and \( d=\frac{1}{2} \) into \( a_n = a_1 + (n - 1)d \):
\[

$$\begin{align*} a_n&=-2+(n - 1)\times\frac{1}{2}\\ &=-2+\frac{n}{2}-\frac{1}{2}\\ &=\frac{n}{2}-\frac{5}{2} \end{align*}$$

\]

Answer:

\( a_n=\frac{1}{2}n - \frac{5}{2} \) (or equivalent forms like \( a_n = 0.5n-2.5 \))