Sequence Analysis: Is -100 an Element of -10n?

Is the number -100 an element of the following sequence?

$-10n$

To determine if the number $-100$ is part of the sequence defined by $-10n$, we follow these steps:

• Step 1: Set up the equation based on the sequence formula.
  We have the formula $-10n$ for the sequence, and we need to find if there exists an integer $n$ such that $-10n = -100$.
• Step 2: Solve the equation for $n$.
  $-10n = -100$.
  To isolate $n$, divide both sides of the equation by $-10$:
  $n = \frac{-100}{-10}$.
  $n = 10$.
• Step 3: Verify if $n$ is a valid index.
  Since $n = 10$ is a positive integer, this means that $-100$ is indeed an element of the sequence.

As $n = 10$, $-100$ is the tenth element in the sequence $-10n$.

Therefore, the solution to the problem is that yes, $-100$ is an element of the sequence, specifically the tenth element. This corresponds to the answer choice: Yes, it is the tenth element.