What is the 507th term of the sequence 1 -1 2 -2 1 -1 2 -2 1…?

Options

A. -1
B. 1
C. -2
D. 2

Answer

To find the 507th term of the sequence 1, -1, 2, -2, 1, -1, 2, -2, ..., we first need to identify the pattern in the sequence.

### Step 1: Identify the repeating pattern
The sequence can be observed as:
1. 1
2. -1
3. 2
4. -2

This pattern of four terms (1, -1, 2, -2) repeats indefinitely.

### Step 2: Determine the position within the pattern
Since the sequence repeats every 4 terms, we can find the position of the 507th term within this repeating cycle by calculating the remainder when 507 is divided by 4.

\[ 507 \div 4 = 126 \quad \text{(quotient)} \]
\[ 507 \mod 4 = 3 \quad \text{(remainder)} \]

### Step 3: Identify the term corresponding to the remainder
The remainder tells us the position in the repeating sequence:
- A remainder of 1 corresponds to the 1st term (1).
- A remainder of 2 corresponds to the 2nd term (-1).
- A remainder of 3 corresponds to the 3rd term (2).
- A remainder of 0 corresponds to the 4th term (-2).

Since the remainder is 3, the 507th term corresponds to the 3rd term of the pattern.

### Step 4: Write down the answer
Thus, the 507th term of the sequence is:

\[ \text{507th term} = 2 \]

### Final Answer:
The 507th term of the sequence is **2**.

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