Question

find the 87th term of the arithmetic sequence 12, 0, -12, ...

Explanation:

Step1: Identify the formula for arithmetic sequence

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, \(d\) is the common difference, and \(n\) is the term number.

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

Here, \(a_1 = 12\). To find \(d\), subtract the first term from the second term: \(d = 0 - 12 = -12\).

Step3: Substitute values into the formula for \(n = 87\)

Substitute \(a_1 = 12\), \(d = -12\), and \(n = 87\) into \(a_n = a_1 + (n - 1)d\):

$$
LATEXBLOCK0
$$

Answer:

\(-1020\)