Third term of sequence `a_n=(-1)^n(n-7)` is:

Options

A. 8
B. -8
C. 4
D. -4

Answer

To find the third term of the sequence defined by \( a_n = (-1)^n (n - 7) \), we will substitute \( n = 3 \) into the formula.

### Step 1: Substitute \( n = 3 \) into the formula
\[ a_3 = (-1)^3 (3 - 7) \]

### Step 2: Calculate \( (-1)^3 \)
Since \( 3 \) is an odd number, \( (-1)^3 = -1 \).

### Step 3: Calculate \( 3 - 7 \)
\[ 3 - 7 = -4 \]

### Step 4: Multiply the results from Step 2 and Step 3
\[ a_3 = -1 \times (-4) = 4 \]

Thus, the third term of the sequence \( a_n \) is \( 4 \).

### Final Answer:
The third term of the sequence is \( 4 \).

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