Question

write an equation for the nth term of the arithmetic sequence -1, -3, -5, -7, ...

Explanation:

Step1: Recall Arithmetic Sequence Formula

The formula for the \( n \)-th 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 \(-1, -3, -5, -7, \dots\), the first term \( a_1 = -1 \). The common difference \( d \) is \( -3 - (-1) = -2 \) (or \( -5 - (-3) = -2 \), etc.).

Step3: Substitute into Formula

Substitute \( a_1 = -1 \) and \( d = -2 \) into the formula:
\( a_n = -1 + (n - 1)(-2) \).
Simplify:
\( a_n = -1 - 2n + 2 = 1 - 2n \).

Answer:

The equation for the \( n \)-th term is \( a_n = 1 - 2n \) (or \( a_n = -2n + 1 \))