Finding the Third Term of a Sequence

The question asks us to find the third term of the sequence defined by the formula $a_n = (-1)^n(n - 7)$.

A sequence is a list of numbers in a specific order. Each number in the sequence is called a term. The formula given, $a_n$, tells us how to find any term of the sequence if we know its position, $n$.

In this formula:

• $a_n$ represents the $n$-th term of the sequence.
• $n$ represents the position of the term in the sequence (e.g., $n=1$ for the first term, $n=2$ for the second term, $n=3$ for the third term, and so on).
• $(-1)^n$ is a part that makes the sign of the term alternate (positive, negative, positive, negative...).
• $(n - 7)$ is another part that depends on the position of the term.

Calculating the Third Term

To find the third term, we need to substitute $n = 3$ into the formula for $a_n$.

The formula is: $a_n = (-1)^n(n - 7)$

Substitute $n = 3$: $a_3 = (-1)^3(3 - 7)$

Now, let's calculate the values step by step:

• First, calculate $(-1)^3$. When -1 is raised to an odd power, the result is -1. So, $(-1)^3 = -1$.
• Next, calculate $(3 - 7)$. $3 - 7 = -4$.
• Now, multiply the results from the previous steps: $(-1) \times (-4)$.
• A negative number multiplied by a negative number gives a positive number. So, $(-1) \times (-4) = 4$.

Therefore, the third term of the sequence is 4.

Let's check this against the given options:

• Option 1: 8
• Option 2: -8
• Option 3: 4
• Option 4: -4

Our calculated value, 4, matches Option 3.